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class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Earliest_results"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.1</span> <span>Earliest results</span> </div> </a> <ul id="toc-Earliest_results-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Foundation" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Foundation"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.2</span> <span>Foundation</span> </div> </a> <ul id="toc-Foundation-sublist" class="vector-toc-list"> <li id="toc-Prize-winning_achievements" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Prize-winning_achievements"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.2.1</span> <span>Prize-winning achievements</span> </div> </a> <ul id="toc-Prize-winning_achievements-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> </ul> </li> <li id="toc-Different_types_of_games" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Different_types_of_games"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>Different types of games</span> </div> </a> <button aria-controls="toc-Different_types_of_games-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Toggle Different types of games subsection</span> </button> <ul id="toc-Different_types_of_games-sublist" class="vector-toc-list"> <li id="toc-Cooperative_/_non-cooperative" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Cooperative_/_non-cooperative"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.1</span> <span>Cooperative / non-cooperative</span> </div> </a> <ul id="toc-Cooperative_/_non-cooperative-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Symmetric_/_asymmetric" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Symmetric_/_asymmetric"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.2</span> <span>Symmetric / asymmetric</span> </div> </a> <ul id="toc-Symmetric_/_asymmetric-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Zero-sum_/_non-zero-sum" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Zero-sum_/_non-zero-sum"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.3</span> <span>Zero-sum / non-zero-sum</span> </div> </a> <ul id="toc-Zero-sum_/_non-zero-sum-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Simultaneous_/_sequential" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Simultaneous_/_sequential"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.4</span> <span>Simultaneous / sequential</span> </div> </a> <ul id="toc-Simultaneous_/_sequential-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Perfect_information_and_imperfect_information" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Perfect_information_and_imperfect_information"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.5</span> <span>Perfect information and imperfect information</span> </div> </a> <ul id="toc-Perfect_information_and_imperfect_information-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Bayesian_game" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Bayesian_game"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.6</span> <span>Bayesian game</span> </div> </a> <ul id="toc-Bayesian_game-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Combinatorial_games" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Combinatorial_games"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.7</span> <span>Combinatorial games</span> </div> </a> <ul id="toc-Combinatorial_games-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Discrete_and_continuous_games" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Discrete_and_continuous_games"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.8</span> <span>Discrete and continuous games</span> </div> </a> <ul id="toc-Discrete_and_continuous_games-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Differential_games" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Differential_games"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.9</span> <span>Differential games</span> </div> </a> <ul id="toc-Differential_games-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Evolutionary_game_theory" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Evolutionary_game_theory"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.10</span> <span>Evolutionary game theory</span> </div> </a> <ul id="toc-Evolutionary_game_theory-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Stochastic_outcomes_(and_relation_to_other_fields)" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Stochastic_outcomes_(and_relation_to_other_fields)"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.11</span> <span>Stochastic outcomes (and relation to other fields)</span> </div> </a> <ul id="toc-Stochastic_outcomes_(and_relation_to_other_fields)-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Metagames" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Metagames"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.12</span> <span>Metagames</span> </div> </a> <ul id="toc-Metagames-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Mean_field_game_theory" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Mean_field_game_theory"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.13</span> <span>Mean field game theory</span> </div> </a> <ul id="toc-Mean_field_game_theory-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Representation_of_games" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Representation_of_games"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Representation of games</span> </div> </a> <button aria-controls="toc-Representation_of_games-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Toggle Representation of games subsection</span> </button> <ul id="toc-Representation_of_games-sublist" class="vector-toc-list"> <li id="toc-Extensive_form" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Extensive_form"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.1</span> <span>Extensive form</span> </div> </a> <ul id="toc-Extensive_form-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Normal_form" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Normal_form"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.2</span> <span>Normal form</span> </div> </a> <ul id="toc-Normal_form-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Characteristic_function_form" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Characteristic_function_form"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.3</span> <span>Characteristic function form</span> </div> </a> <ul id="toc-Characteristic_function_form-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Alternative_game_representations" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Alternative_game_representations"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.4</span> <span>Alternative game representations</span> </div> </a> <ul id="toc-Alternative_game_representations-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-General_and_applied_uses" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#General_and_applied_uses"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>General and applied uses</span> </div> </a> <button aria-controls="toc-General_and_applied_uses-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Toggle General and applied uses subsection</span> </button> <ul id="toc-General_and_applied_uses-sublist" class="vector-toc-list"> <li id="toc-Description_and_modeling" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Description_and_modeling"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.1</span> <span>Description and modeling</span> </div> </a> <ul id="toc-Description_and_modeling-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Prescriptive_or_normative_analysis" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Prescriptive_or_normative_analysis"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.2</span> <span>Prescriptive or normative analysis</span> </div> </a> <ul id="toc-Prescriptive_or_normative_analysis-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Economics" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Economics"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.3</span> <span>Economics</span> </div> </a> <ul id="toc-Economics-sublist" class="vector-toc-list"> <li id="toc-Managerial_economics" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Managerial_economics"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.3.1</span> <span>Managerial economics</span> </div> </a> <ul id="toc-Managerial_economics-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Business" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Business"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.4</span> <span>Business</span> </div> </a> <ul id="toc-Business-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Project_management" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Project_management"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.5</span> <span>Project management</span> </div> </a> <ul id="toc-Project_management-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Political_science" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Political_science"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.6</span> <span>Political science</span> </div> </a> <ul id="toc-Political_science-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Defence_science_and_technology" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Defence_science_and_technology"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.7</span> <span>Defence science and technology</span> </div> </a> <ul id="toc-Defence_science_and_technology-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Biology" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Biology"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.8</span> <span>Biology</span> </div> </a> <ul id="toc-Biology-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Computer_science_and_logic" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Computer_science_and_logic"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.9</span> <span>Computer science and logic</span> </div> </a> <ul id="toc-Computer_science_and_logic-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Philosophy" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Philosophy"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.10</span> <span>Philosophy</span> </div> </a> <ul id="toc-Philosophy-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Epidemiology" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Epidemiology"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.11</span> <span>Epidemiology</span> </div> </a> <ul id="toc-Epidemiology-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Well_known_examples_of_games" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Well_known_examples_of_games"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>Well known examples of games</span> </div> </a> <button aria-controls="toc-Well_known_examples_of_games-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Toggle Well known examples of games subsection</span> </button> <ul id="toc-Well_known_examples_of_games-sublist" class="vector-toc-list"> <li id="toc-Prisoner's_dilemma" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Prisoner's_dilemma"> <div class="vector-toc-text"> <span class="vector-toc-numb">5.1</span> <span>Prisoner's dilemma</span> </div> </a> <ul id="toc-Prisoner's_dilemma-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Battle_of_the_sexes" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Battle_of_the_sexes"> <div class="vector-toc-text"> <span class="vector-toc-numb">5.2</span> <span>Battle of the sexes</span> </div> </a> <ul id="toc-Battle_of_the_sexes-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Ultimatum_game" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Ultimatum_game"> <div class="vector-toc-text"> <span class="vector-toc-numb">5.3</span> <span>Ultimatum game</span> </div> </a> <ul id="toc-Ultimatum_game-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Trust_game" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Trust_game"> <div class="vector-toc-text"> <span class="vector-toc-numb">5.4</span> <span>Trust game</span> </div> </a> <ul id="toc-Trust_game-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Cournot_Competition" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Cournot_Competition"> <div class="vector-toc-text"> <span class="vector-toc-numb">5.5</span> <span>Cournot Competition</span> </div> </a> <ul id="toc-Cournot_Competition-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Bertrand_Competition" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Bertrand_Competition"> <div class="vector-toc-text"> <span class="vector-toc-numb">5.6</span> <span>Bertrand Competition</span> </div> </a> <ul id="toc-Bertrand_Competition-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-In_popular_culture" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#In_popular_culture"> <div class="vector-toc-text"> <span class="vector-toc-numb">6</span> <span>In popular culture</span> </div> </a> <ul id="toc-In_popular_culture-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-See_also" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#See_also"> <div class="vector-toc-text"> <span class="vector-toc-numb">7</span> <span>See also</span> </div> </a> <ul id="toc-See_also-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Notes" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Notes"> <div class="vector-toc-text"> <span class="vector-toc-numb">8</span> <span>Notes</span> </div> </a> <ul id="toc-Notes-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-References" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#References"> <div class="vector-toc-text"> <span class="vector-toc-numb">9</span> <span>References</span> </div> </a> <ul id="toc-References-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Sources" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Sources"> <div class="vector-toc-text"> <span class="vector-toc-numb">10</span> <span>Sources</span> </div> </a> <ul id="toc-Sources-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Further_reading" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Further_reading"> <div class="vector-toc-text"> <span class="vector-toc-numb">11</span> <span>Further reading</span> </div> </a> <button aria-controls="toc-Further_reading-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Toggle Further reading subsection</span> </button> <ul id="toc-Further_reading-sublist" class="vector-toc-list"> <li id="toc-Textbooks_and_general_literature" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Textbooks_and_general_literature"> <div class="vector-toc-text"> <span class="vector-toc-numb">11.1</span> <span>Textbooks and general literature</span> </div> </a> <ul id="toc-Textbooks_and_general_literature-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Historically_important_texts" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Historically_important_texts"> <div class="vector-toc-text"> <span class="vector-toc-numb">11.2</span> <span>Historically important texts</span> </div> </a> <ul id="toc-Historically_important_texts-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Other_material" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Other_material"> <div class="vector-toc-text"> <span class="vector-toc-numb">11.3</span> <span>Other material</span> </div> </a> <ul id="toc-Other_material-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-External_links" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#External_links"> <div class="vector-toc-text"> <span class="vector-toc-numb">12</span> <span>External links</span> </div> </a> <ul id="toc-External_links-sublist" class="vector-toc-list"> </ul> </li> </ul> </div> </div> </nav> </div> </div> <div class="mw-content-container"> <main id="content" class="mw-body"> <header class="mw-body-header vector-page-titlebar"> <nav aria-label="Contents" class="vector-toc-landmark"> <div id="vector-page-titlebar-toc" class="vector-dropdown vector-page-titlebar-toc vector-button-flush-left" > <input type="checkbox" id="vector-page-titlebar-toc-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-page-titlebar-toc" class="vector-dropdown-checkbox " aria-label="Toggle the table of contents" > <label id="vector-page-titlebar-toc-label" for="vector-page-titlebar-toc-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only " aria-hidden="true" ><span class="vector-icon mw-ui-icon-listBullet mw-ui-icon-wikimedia-listBullet"></span> <span class="vector-dropdown-label-text">Toggle the table of contents</span> </label> <div class="vector-dropdown-content"> <div id="vector-page-titlebar-toc-unpinned-container" class="vector-unpinned-container"> </div> </div> </div> </nav> <h1 id="firstHeading" class="firstHeading mw-first-heading"><span class="mw-page-title-main">Game theory</span></h1> <div id="p-lang-btn" class="vector-dropdown mw-portlet mw-portlet-lang" > <input type="checkbox" id="p-lang-btn-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-p-lang-btn" class="vector-dropdown-checkbox mw-interlanguage-selector" aria-label="Go to an article in another language. Available in 86 languages" > <label id="p-lang-btn-label" for="p-lang-btn-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--action-progressive mw-portlet-lang-heading-86" aria-hidden="true" ><span class="vector-icon mw-ui-icon-language-progressive mw-ui-icon-wikimedia-language-progressive"></span> <span class="vector-dropdown-label-text">86 languages</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D9%86%D8%B8%D8%B1%D9%8A%D8%A9_%D8%A7%D9%84%D8%A3%D9%84%D8%B9%D8%A7%D8%A8" title="نظرية الألعاب – Arabic" lang="ar" hreflang="ar" data-title="نظرية الألعاب" data-language-autonym="العربية" data-language-local-name="Arabic" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-ast mw-list-item"><a href="https://ast.wikipedia.org/wiki/Teor%C3%ADa_de_xuegos" title="Teoría de xuegos – Asturian" lang="ast" hreflang="ast" data-title="Teoría de xuegos" data-language-autonym="Asturianu" data-language-local-name="Asturian" class="interlanguage-link-target"><span>Asturianu</span></a></li><li class="interlanguage-link interwiki-az mw-list-item"><a href="https://az.wikipedia.org/wiki/Oyunlar_n%C9%99z%C9%99riyy%C9%99si" title="Oyunlar nəzəriyyəsi – Azerbaijani" lang="az" hreflang="az" data-title="Oyunlar nəzəriyyəsi" data-language-autonym="Azərbaycanca" data-language-local-name="Azerbaijani" class="interlanguage-link-target"><span>Azərbaycanca</span></a></li><li class="interlanguage-link interwiki-azb mw-list-item"><a href="https://azb.wikipedia.org/wiki/%D8%A7%D9%88%DB%8C%D9%88%D9%86_%D8%AA%D8%A6%D9%88%D8%B1%DB%8C%D8%B3%DB%8C" title="اویون تئوریسی – South Azerbaijani" lang="azb" hreflang="azb" data-title="اویون تئوریسی" data-language-autonym="تۆرکجه" data-language-local-name="South Azerbaijani" class="interlanguage-link-target"><span>تۆرکجه</span></a></li><li class="interlanguage-link interwiki-bn mw-list-item"><a href="https://bn.wikipedia.org/wiki/%E0%A6%95%E0%A7%8D%E0%A6%B0%E0%A7%80%E0%A6%A1%E0%A6%BC%E0%A6%BE_%E0%A6%A4%E0%A6%A4%E0%A7%8D%E0%A6%A4%E0%A7%8D%E0%A6%AC" title="ক্রীড়া তত্ত্ব – Bangla" lang="bn" hreflang="bn" data-title="ক্রীড়া তত্ত্ব" data-language-autonym="বাংলা" data-language-local-name="Bangla" class="interlanguage-link-target"><span>বাংলা</span></a></li><li class="interlanguage-link interwiki-zh-min-nan mw-list-item"><a href="https://zh-min-nan.wikipedia.org/wiki/I%C3%BB-h%C3%AC_l%C3%AD-l%C5%ABn" title="Iû-hì lí-lūn – Minnan" lang="nan" hreflang="nan" data-title="Iû-hì lí-lūn" data-language-autonym="閩南語 / Bân-lâm-gú" data-language-local-name="Minnan" class="interlanguage-link-target"><span>閩南語 / Bân-lâm-gú</span></a></li><li class="interlanguage-link interwiki-be mw-list-item"><a href="https://be.wikipedia.org/wiki/%D0%A2%D1%8D%D0%BE%D1%80%D1%8B%D1%8F_%D0%B3%D1%83%D0%BB%D1%8C%D0%BD%D1%8F%D1%9E" title="Тэорыя гульняў – Belarusian" lang="be" hreflang="be" data-title="Тэорыя гульняў" data-language-autonym="Беларуская" data-language-local-name="Belarusian" class="interlanguage-link-target"><span>Беларуская</span></a></li><li class="interlanguage-link interwiki-bg mw-list-item"><a href="https://bg.wikipedia.org/wiki/%D0%A2%D0%B5%D0%BE%D1%80%D0%B8%D1%8F_%D0%BD%D0%B0_%D0%B8%D0%B3%D1%80%D0%B8%D1%82%D0%B5" title="Теория на игрите – Bulgarian" lang="bg" hreflang="bg" data-title="Теория на игрите" data-language-autonym="Български" data-language-local-name="Bulgarian" class="interlanguage-link-target"><span>Български</span></a></li><li class="interlanguage-link interwiki-bar mw-list-item"><a href="https://bar.wikipedia.org/wiki/Spuitheorie" title="Spuitheorie – Bavarian" lang="bar" hreflang="bar" data-title="Spuitheorie" data-language-autonym="Boarisch" data-language-local-name="Bavarian" class="interlanguage-link-target"><span>Boarisch</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/Teoria_dels_jocs" title="Teoria dels jocs – Catalan" lang="ca" hreflang="ca" data-title="Teoria dels jocs" data-language-autonym="Català" data-language-local-name="Catalan" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-cs mw-list-item"><a href="https://cs.wikipedia.org/wiki/Teorie_her" title="Teorie her – Czech" lang="cs" hreflang="cs" data-title="Teorie her" data-language-autonym="Čeština" data-language-local-name="Czech" class="interlanguage-link-target"><span>Čeština</span></a></li><li class="interlanguage-link interwiki-cy mw-list-item"><a href="https://cy.wikipedia.org/wiki/Damcaniaeth_gemau" title="Damcaniaeth gemau – Welsh" lang="cy" hreflang="cy" data-title="Damcaniaeth gemau" data-language-autonym="Cymraeg" data-language-local-name="Welsh" class="interlanguage-link-target"><span>Cymraeg</span></a></li><li class="interlanguage-link interwiki-da mw-list-item"><a href="https://da.wikipedia.org/wiki/Spilteori" title="Spilteori – Danish" lang="da" hreflang="da" data-title="Spilteori" data-language-autonym="Dansk" data-language-local-name="Danish" class="interlanguage-link-target"><span>Dansk</span></a></li><li class="interlanguage-link interwiki-pdc mw-list-item"><a href="https://pdc.wikipedia.org/wiki/Schpiel-Theory" title="Schpiel-Theory – Pennsylvania German" lang="pdc" hreflang="pdc" data-title="Schpiel-Theory" data-language-autonym="Deitsch" data-language-local-name="Pennsylvania German" class="interlanguage-link-target"><span>Deitsch</span></a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Spieltheorie" title="Spieltheorie – German" lang="de" hreflang="de" data-title="Spieltheorie" data-language-autonym="Deutsch" data-language-local-name="German" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-et mw-list-item"><a href="https://et.wikipedia.org/wiki/M%C3%A4nguteooria" title="Mänguteooria – Estonian" lang="et" hreflang="et" data-title="Mänguteooria" data-language-autonym="Eesti" data-language-local-name="Estonian" class="interlanguage-link-target"><span>Eesti</span></a></li><li class="interlanguage-link interwiki-el mw-list-item"><a href="https://el.wikipedia.org/wiki/%CE%98%CE%B5%CF%89%CF%81%CE%AF%CE%B1_%CF%80%CE%B1%CE%B9%CE%B3%CE%BD%CE%AF%CF%89%CE%BD" title="Θεωρία παιγνίων – Greek" lang="el" hreflang="el" data-title="Θεωρία παιγνίων" data-language-autonym="Ελληνικά" data-language-local-name="Greek" class="interlanguage-link-target"><span>Ελληνικά</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/Teor%C3%ADa_de_juegos" title="Teoría de juegos – Spanish" lang="es" hreflang="es" data-title="Teoría de juegos" data-language-autonym="Español" data-language-local-name="Spanish" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-eo mw-list-item"><a href="https://eo.wikipedia.org/wiki/Ludoteorio" title="Ludoteorio – Esperanto" lang="eo" hreflang="eo" data-title="Ludoteorio" data-language-autonym="Esperanto" data-language-local-name="Esperanto" class="interlanguage-link-target"><span>Esperanto</span></a></li><li class="interlanguage-link interwiki-eu mw-list-item"><a href="https://eu.wikipedia.org/wiki/Joko-teoria" title="Joko-teoria – Basque" lang="eu" hreflang="eu" data-title="Joko-teoria" data-language-autonym="Euskara" data-language-local-name="Basque" class="interlanguage-link-target"><span>Euskara</span></a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%D9%86%D8%B8%D8%B1%DB%8C%D9%87_%D8%A8%D8%A7%D8%B2%DB%8C" title="نظریه بازی – Persian" lang="fa" hreflang="fa" data-title="نظریه بازی" data-language-autonym="فارسی" data-language-local-name="Persian" class="interlanguage-link-target"><span>فارسی</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/Th%C3%A9orie_des_jeux" title="Théorie des jeux – French" lang="fr" hreflang="fr" data-title="Théorie des jeux" data-language-autonym="Français" data-language-local-name="French" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-ga mw-list-item"><a href="https://ga.wikipedia.org/wiki/Teoiric_na_gcluich%C3%AD" title="Teoiric na gcluichí – Irish" lang="ga" hreflang="ga" data-title="Teoiric na gcluichí" data-language-autonym="Gaeilge" data-language-local-name="Irish" class="interlanguage-link-target"><span>Gaeilge</span></a></li><li class="interlanguage-link interwiki-gl mw-list-item"><a href="https://gl.wikipedia.org/wiki/Teor%C3%ADa_de_xogos" title="Teoría de xogos – Galician" lang="gl" hreflang="gl" data-title="Teoría de xogos" data-language-autonym="Galego" data-language-local-name="Galician" class="interlanguage-link-target"><span>Galego</span></a></li><li class="interlanguage-link interwiki-gan mw-list-item"><a href="https://gan.wikipedia.org/wiki/%E5%8D%9A%E5%BC%88%E8%AB%96" title="博弈論 – Gan" lang="gan" hreflang="gan" data-title="博弈論" data-language-autonym="贛語" data-language-local-name="Gan" class="interlanguage-link-target"><span>贛語</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%EA%B2%8C%EC%9E%84_%EC%9D%B4%EB%A1%A0" title="게임 이론 – Korean" lang="ko" hreflang="ko" data-title="게임 이론" data-language-autonym="한국어" data-language-local-name="Korean" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-hy mw-list-item"><a href="https://hy.wikipedia.org/wiki/%D4%BD%D5%A1%D5%B2%D5%A5%D6%80%D5%AB_%D5%BF%D5%A5%D5%BD%D5%B8%D6%82%D5%A9%D5%B5%D5%B8%D6%82%D5%B6" title="Խաղերի տեսություն – Armenian" lang="hy" hreflang="hy" data-title="Խաղերի տեսություն" data-language-autonym="Հայերեն" data-language-local-name="Armenian" class="interlanguage-link-target"><span>Հայերեն</span></a></li><li class="interlanguage-link interwiki-hi mw-list-item"><a href="https://hi.wikipedia.org/wiki/%E0%A4%96%E0%A5%87%E0%A4%B2_%E0%A4%B8%E0%A4%BF%E0%A4%A6%E0%A5%8D%E0%A4%A7%E0%A4%BE%E0%A4%82%E0%A4%A4" title="खेल सिद्धांत – Hindi" lang="hi" hreflang="hi" data-title="खेल सिद्धांत" data-language-autonym="हिन्दी" data-language-local-name="Hindi" class="interlanguage-link-target"><span>हिन्दी</span></a></li><li class="interlanguage-link interwiki-hr mw-list-item"><a href="https://hr.wikipedia.org/wiki/Teorija_igara" title="Teorija igara – Croatian" lang="hr" hreflang="hr" data-title="Teorija igara" data-language-autonym="Hrvatski" data-language-local-name="Croatian" class="interlanguage-link-target"><span>Hrvatski</span></a></li><li class="interlanguage-link interwiki-io mw-list-item"><a href="https://io.wikipedia.org/wiki/Ludo-teorio" title="Ludo-teorio – Ido" lang="io" hreflang="io" data-title="Ludo-teorio" data-language-autonym="Ido" data-language-local-name="Ido" class="interlanguage-link-target"><span>Ido</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Teori_permainan" title="Teori permainan – Indonesian" lang="id" hreflang="id" data-title="Teori permainan" data-language-autonym="Bahasa Indonesia" data-language-local-name="Indonesian" class="interlanguage-link-target"><span>Bahasa Indonesia</span></a></li><li class="interlanguage-link interwiki-ia mw-list-item"><a href="https://ia.wikipedia.org/wiki/Theoria_de_jocos" title="Theoria de jocos – Interlingua" lang="ia" hreflang="ia" data-title="Theoria de jocos" data-language-autonym="Interlingua" data-language-local-name="Interlingua" class="interlanguage-link-target"><span>Interlingua</span></a></li><li class="interlanguage-link interwiki-is mw-list-item"><a href="https://is.wikipedia.org/wiki/Leikjafr%C3%A6%C3%B0i" title="Leikjafræði – Icelandic" lang="is" hreflang="is" data-title="Leikjafræði" data-language-autonym="Íslenska" data-language-local-name="Icelandic" class="interlanguage-link-target"><span>Íslenska</span></a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Teoria_dei_giochi" title="Teoria dei giochi – Italian" lang="it" hreflang="it" data-title="Teoria dei giochi" data-language-autonym="Italiano" data-language-local-name="Italian" class="interlanguage-link-target"><span>Italiano</span></a></li><li class="interlanguage-link interwiki-he mw-list-item"><a href="https://he.wikipedia.org/wiki/%D7%AA%D7%95%D7%A8%D7%AA_%D7%94%D7%9E%D7%A9%D7%97%D7%A7%D7%99%D7%9D" title="תורת המשחקים – Hebrew" lang="he" hreflang="he" data-title="תורת המשחקים" data-language-autonym="עברית" data-language-local-name="Hebrew" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-ka mw-list-item"><a href="https://ka.wikipedia.org/wiki/%E1%83%97%E1%83%90%E1%83%9B%E1%83%90%E1%83%A8%E1%83%97%E1%83%90_%E1%83%97%E1%83%94%E1%83%9D%E1%83%A0%E1%83%98%E1%83%90" title="თამაშთა თეორია – Georgian" lang="ka" hreflang="ka" data-title="თამაშთა თეორია" data-language-autonym="ქართული" data-language-local-name="Georgian" class="interlanguage-link-target"><span>ქართული</span></a></li><li class="interlanguage-link interwiki-kk mw-list-item"><a href="https://kk.wikipedia.org/wiki/%D0%9E%D0%B9%D1%8B%D0%BD%D0%B4%D0%B0%D1%80_%D1%82%D0%B5%D0%BE%D1%80%D0%B8%D1%8F%D1%81%D1%8B" title="Ойындар теориясы – Kazakh" lang="kk" hreflang="kk" data-title="Ойындар теориясы" data-language-autonym="Қазақша" data-language-local-name="Kazakh" class="interlanguage-link-target"><span>Қазақша</span></a></li><li class="interlanguage-link interwiki-gcr mw-list-item"><a href="https://gcr.wikipedia.org/wiki/T%C3%A9ori_di_s%C3%A9_j%C3%A9" title="Téori di sé jé – Guianan Creole" lang="gcr" hreflang="gcr" data-title="Téori di sé jé" data-language-autonym="Kriyòl gwiyannen" data-language-local-name="Guianan Creole" class="interlanguage-link-target"><span>Kriyòl gwiyannen</span></a></li><li class="interlanguage-link interwiki-ky mw-list-item"><a href="https://ky.wikipedia.org/wiki/%D0%9E%D1%8E%D0%BD%D0%B4%D0%B0%D1%80_%D1%82%D0%B5%D0%BE%D1%80%D0%B8%D1%8F%D1%81%D1%8B" title="Оюндар теориясы – Kyrgyz" lang="ky" hreflang="ky" data-title="Оюндар теориясы" data-language-autonym="Кыргызча" data-language-local-name="Kyrgyz" class="interlanguage-link-target"><span>Кыргызча</span></a></li><li class="interlanguage-link interwiki-lv mw-list-item"><a href="https://lv.wikipedia.org/wiki/Sp%C4%93%C4%BCu_teorija" title="Spēļu teorija – Latvian" lang="lv" hreflang="lv" data-title="Spēļu teorija" data-language-autonym="Latviešu" data-language-local-name="Latvian" class="interlanguage-link-target"><span>Latviešu</span></a></li><li class="interlanguage-link interwiki-lt mw-list-item"><a href="https://lt.wikipedia.org/wiki/%C5%BDaidim%C5%B3_teorija" title="Žaidimų teorija – Lithuanian" lang="lt" hreflang="lt" data-title="Žaidimų teorija" data-language-autonym="Lietuvių" data-language-local-name="Lithuanian" class="interlanguage-link-target"><span>Lietuvių</span></a></li><li class="interlanguage-link interwiki-hu mw-list-item"><a href="https://hu.wikipedia.org/wiki/J%C3%A1t%C3%A9kelm%C3%A9let" title="Játékelmélet – Hungarian" lang="hu" hreflang="hu" data-title="Játékelmélet" data-language-autonym="Magyar" data-language-local-name="Hungarian" class="interlanguage-link-target"><span>Magyar</span></a></li><li class="interlanguage-link interwiki-mk mw-list-item"><a href="https://mk.wikipedia.org/wiki/%D0%A2%D0%B5%D0%BE%D1%80%D0%B8%D1%98%D0%B0_%D0%BD%D0%B0_%D0%B8%D0%B3%D1%80%D0%B8" title="Теорија на игри – Macedonian" lang="mk" hreflang="mk" data-title="Теорија на игри" data-language-autonym="Македонски" data-language-local-name="Macedonian" class="interlanguage-link-target"><span>Македонски</span></a></li><li class="interlanguage-link interwiki-ml mw-list-item"><a href="https://ml.wikipedia.org/wiki/%E0%B4%AE%E0%B4%A4%E0%B5%8D%E0%B4%B8%E0%B4%B0_%E0%B4%B8%E0%B4%BF%E0%B4%A6%E0%B5%8D%E0%B4%A7%E0%B4%BE%E0%B4%A8%E0%B5%8D%E0%B4%A4%E0%B4%82" title="മത്സര സിദ്ധാന്തം – Malayalam" lang="ml" hreflang="ml" data-title="മത്സര സിദ്ധാന്തം" data-language-autonym="മലയാളം" data-language-local-name="Malayalam" class="interlanguage-link-target"><span>മലയാളം</span></a></li><li class="interlanguage-link interwiki-ms mw-list-item"><a href="https://ms.wikipedia.org/wiki/Teori_permainan" title="Teori permainan – Malay" lang="ms" hreflang="ms" data-title="Teori permainan" data-language-autonym="Bahasa Melayu" data-language-local-name="Malay" class="interlanguage-link-target"><span>Bahasa Melayu</span></a></li><li class="interlanguage-link interwiki-mn mw-list-item"><a href="https://mn.wikipedia.org/wiki/%D0%A2%D0%BE%D0%B3%D0%BB%D0%BE%D0%BE%D0%BC%D1%8B%D0%BD_%D0%BE%D0%BD%D0%BE%D0%BB" title="Тоглоомын онол – Mongolian" lang="mn" hreflang="mn" data-title="Тоглоомын онол" data-language-autonym="Монгол" data-language-local-name="Mongolian" class="interlanguage-link-target"><span>Монгол</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Speltheorie" title="Speltheorie – Dutch" lang="nl" hreflang="nl" data-title="Speltheorie" data-language-autonym="Nederlands" data-language-local-name="Dutch" class="interlanguage-link-target"><span>Nederlands</span></a></li><li class="interlanguage-link interwiki-ja badge-Q17437798 badge-goodarticle mw-list-item" title="good article badge"><a href="https://ja.wikipedia.org/wiki/%E3%82%B2%E3%83%BC%E3%83%A0%E7%90%86%E8%AB%96" title="ゲーム理論 – Japanese" lang="ja" hreflang="ja" data-title="ゲーム理論" data-language-autonym="日本語" data-language-local-name="Japanese" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-no mw-list-item"><a href="https://no.wikipedia.org/wiki/Spillteori" title="Spillteori – Norwegian Bokmål" lang="nb" hreflang="nb" data-title="Spillteori" data-language-autonym="Norsk bokmål" data-language-local-name="Norwegian Bokmål" class="interlanguage-link-target"><span>Norsk bokmål</span></a></li><li class="interlanguage-link interwiki-nn mw-list-item"><a href="https://nn.wikipedia.org/wiki/Spelteori" title="Spelteori – Norwegian Nynorsk" lang="nn" hreflang="nn" data-title="Spelteori" data-language-autonym="Norsk nynorsk" data-language-local-name="Norwegian Nynorsk" class="interlanguage-link-target"><span>Norsk nynorsk</span></a></li><li class="interlanguage-link interwiki-nov mw-list-item"><a href="https://nov.wikipedia.org/wiki/Lude-teorie" title="Lude-teorie – Novial" lang="nov" hreflang="nov" data-title="Lude-teorie" data-language-autonym="Novial" data-language-local-name="Novial" class="interlanguage-link-target"><span>Novial</span></a></li><li class="interlanguage-link interwiki-oc mw-list-item"><a href="https://oc.wikipedia.org/wiki/Teoria_dels_j%C3%B2cs" title="Teoria dels jòcs – Occitan" lang="oc" hreflang="oc" data-title="Teoria dels jòcs" data-language-autonym="Occitan" data-language-local-name="Occitan" class="interlanguage-link-target"><span>Occitan</span></a></li><li class="interlanguage-link interwiki-uz mw-list-item"><a href="https://uz.wikipedia.org/wiki/O%CA%BByinlar_nazariyasi" title="Oʻyinlar nazariyasi – Uzbek" lang="uz" hreflang="uz" data-title="Oʻyinlar nazariyasi" data-language-autonym="Oʻzbekcha / ўзбекча" data-language-local-name="Uzbek" class="interlanguage-link-target"><span>Oʻzbekcha / ўзбекча</span></a></li><li class="interlanguage-link interwiki-pa mw-list-item"><a href="https://pa.wikipedia.org/wiki/%E0%A8%97%E0%A9%87%E0%A8%AE_%E0%A8%A5%E0%A8%BF%E0%A8%8A%E0%A8%B0%E0%A9%80" title="ਗੇਮ ਥਿਊਰੀ – Punjabi" lang="pa" hreflang="pa" data-title="ਗੇਮ ਥਿਊਰੀ" data-language-autonym="ਪੰਜਾਬੀ" data-language-local-name="Punjabi" class="interlanguage-link-target"><span>ਪੰਜਾਬੀ</span></a></li><li class="interlanguage-link interwiki-ps mw-list-item"><a href="https://ps.wikipedia.org/wiki/%D8%AF_%D9%84%D9%88%D8%A8%DB%8C_%D9%86%D8%B8%D8%B1%DB%8C%D9%87" title="د لوبی نظریه – Pashto" lang="ps" hreflang="ps" data-title="د لوبی نظریه" data-language-autonym="پښتو" data-language-local-name="Pashto" class="interlanguage-link-target"><span>پښتو</span></a></li><li class="interlanguage-link interwiki-jam mw-list-item"><a href="https://jam.wikipedia.org/wiki/Giem_tiori" title="Giem tiori – Jamaican Creole English" lang="jam" hreflang="jam" data-title="Giem tiori" data-language-autonym="Patois" data-language-local-name="Jamaican Creole English" class="interlanguage-link-target"><span>Patois</span></a></li><li class="interlanguage-link interwiki-km mw-list-item"><a href="https://km.wikipedia.org/wiki/%E1%9E%91%E1%9F%92%E1%9E%9A%E1%9E%B9%E1%9E%9F%E1%9F%92%E1%9E%8A%E1%9E%B8%E1%9E%9B%E1%9F%92%E1%9E%94%E1%9F%82%E1%9E%84" title="ទ្រឹស្ដីល្បែង – Khmer" lang="km" hreflang="km" data-title="ទ្រឹស្ដីល្បែង" data-language-autonym="ភាសាខ្មែរ" data-language-local-name="Khmer" class="interlanguage-link-target"><span>ភាសាខ្មែរ</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Teoria_gier" title="Teoria gier – Polish" lang="pl" hreflang="pl" data-title="Teoria gier" data-language-autonym="Polski" data-language-local-name="Polish" class="interlanguage-link-target"><span>Polski</span></a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/Teoria_dos_jogos" title="Teoria dos jogos – Portuguese" lang="pt" hreflang="pt" data-title="Teoria dos jogos" data-language-autonym="Português" data-language-local-name="Portuguese" class="interlanguage-link-target"><span>Português</span></a></li><li class="interlanguage-link interwiki-ro mw-list-item"><a href="https://ro.wikipedia.org/wiki/Teoria_jocurilor" title="Teoria jocurilor – Romanian" lang="ro" hreflang="ro" data-title="Teoria jocurilor" data-language-autonym="Română" data-language-local-name="Romanian" class="interlanguage-link-target"><span>Română</span></a></li><li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/%D0%A2%D0%B5%D0%BE%D1%80%D0%B8%D1%8F_%D0%B8%D0%B3%D1%80" title="Теория игр – Russian" lang="ru" hreflang="ru" data-title="Теория игр" data-language-autonym="Русский" data-language-local-name="Russian" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-sq mw-list-item"><a href="https://sq.wikipedia.org/wiki/Teoria_e_loj%C3%ABs" title="Teoria e lojës – Albanian" lang="sq" hreflang="sq" data-title="Teoria e lojës" data-language-autonym="Shqip" data-language-local-name="Albanian" class="interlanguage-link-target"><span>Shqip</span></a></li><li class="interlanguage-link interwiki-scn mw-list-item"><a href="https://scn.wikipedia.org/wiki/Tiur%C3%ACa_di_li_joca" title="Tiurìa di li joca – Sicilian" lang="scn" hreflang="scn" data-title="Tiurìa di li joca" data-language-autonym="Sicilianu" data-language-local-name="Sicilian" class="interlanguage-link-target"><span>Sicilianu</span></a></li><li class="interlanguage-link interwiki-si mw-list-item"><a href="https://si.wikipedia.org/wiki/%E0%B6%9A%E0%B7%8A%E2%80%8D%E0%B6%BB%E0%B7%93%E0%B6%A9%E0%B7%8F_%E0%B6%B1%E0%B7%8A%E2%80%8D%E0%B6%BA%E0%B7%8F%E0%B6%BA" title="ක්‍රීඩා න්‍යාය – Sinhala" lang="si" hreflang="si" data-title="ක්‍රීඩා න්‍යාය" data-language-autonym="සිංහල" data-language-local-name="Sinhala" class="interlanguage-link-target"><span>සිංහල</span></a></li><li class="interlanguage-link interwiki-simple mw-list-item"><a href="https://simple.wikipedia.org/wiki/Game_theory" title="Game theory – Simple English" lang="en-simple" hreflang="en-simple" data-title="Game theory" data-language-autonym="Simple English" data-language-local-name="Simple English" class="interlanguage-link-target"><span>Simple English</span></a></li><li class="interlanguage-link interwiki-sk mw-list-item"><a href="https://sk.wikipedia.org/wiki/Te%C3%B3ria_hier" title="Teória hier – Slovak" lang="sk" hreflang="sk" data-title="Teória hier" data-language-autonym="Slovenčina" data-language-local-name="Slovak" class="interlanguage-link-target"><span>Slovenčina</span></a></li><li class="interlanguage-link interwiki-sl mw-list-item"><a href="https://sl.wikipedia.org/wiki/Teorija_iger" title="Teorija iger – Slovenian" lang="sl" hreflang="sl" data-title="Teorija iger" data-language-autonym="Slovenščina" data-language-local-name="Slovenian" class="interlanguage-link-target"><span>Slovenščina</span></a></li><li class="interlanguage-link interwiki-ckb mw-list-item"><a href="https://ckb.wikipedia.org/wiki/%D8%AA%DB%8C%DB%86%D8%B1%DB%8C%DB%8C_%DA%A9%D8%A7%DB%8C%DB%95" title="تیۆریی کایە – Central Kurdish" lang="ckb" hreflang="ckb" data-title="تیۆریی کایە" data-language-autonym="کوردی" data-language-local-name="Central Kurdish" class="interlanguage-link-target"><span>کوردی</span></a></li><li class="interlanguage-link interwiki-sr mw-list-item"><a href="https://sr.wikipedia.org/wiki/%D0%A2%D0%B5%D0%BE%D1%80%D0%B8%D1%98%D0%B0_%D0%B8%D0%B3%D0%B0%D1%80%D0%B0" title="Теорија игара – Serbian" lang="sr" hreflang="sr" data-title="Теорија игара" data-language-autonym="Српски / srpski" data-language-local-name="Serbian" class="interlanguage-link-target"><span>Српски / srpski</span></a></li><li class="interlanguage-link interwiki-sh mw-list-item"><a href="https://sh.wikipedia.org/wiki/Teorija_igara" title="Teorija igara – Serbo-Croatian" lang="sh" hreflang="sh" data-title="Teorija igara" data-language-autonym="Srpskohrvatski / српскохрватски" data-language-local-name="Serbo-Croatian" class="interlanguage-link-target"><span>Srpskohrvatski / српскохрватски</span></a></li><li class="interlanguage-link interwiki-fi mw-list-item"><a href="https://fi.wikipedia.org/wiki/Peliteoria" title="Peliteoria – Finnish" lang="fi" hreflang="fi" data-title="Peliteoria" data-language-autonym="Suomi" data-language-local-name="Finnish" class="interlanguage-link-target"><span>Suomi</span></a></li><li class="interlanguage-link interwiki-sv mw-list-item"><a href="https://sv.wikipedia.org/wiki/Spelteori" title="Spelteori – Swedish" lang="sv" hreflang="sv" data-title="Spelteori" data-language-autonym="Svenska" data-language-local-name="Swedish" class="interlanguage-link-target"><span>Svenska</span></a></li><li class="interlanguage-link interwiki-tl mw-list-item"><a href="https://tl.wikipedia.org/wiki/Teorya_ng_laro" title="Teorya ng laro – Tagalog" lang="tl" hreflang="tl" data-title="Teorya ng laro" data-language-autonym="Tagalog" data-language-local-name="Tagalog" class="interlanguage-link-target"><span>Tagalog</span></a></li><li class="interlanguage-link interwiki-ta mw-list-item"><a href="https://ta.wikipedia.org/wiki/%E0%AE%86%E0%AE%9F%E0%AF%8D%E0%AE%9F%E0%AE%95%E0%AF%8D_%E0%AE%95%E0%AF%8B%E0%AE%9F%E0%AF%8D%E0%AE%AA%E0%AE%BE%E0%AE%9F%E0%AF%81" title="ஆட்டக் கோட்பாடு – Tamil" lang="ta" hreflang="ta" data-title="ஆட்டக் கோட்பாடு" data-language-autonym="தமிழ்" data-language-local-name="Tamil" class="interlanguage-link-target"><span>தமிழ்</span></a></li><li class="interlanguage-link interwiki-th mw-list-item"><a href="https://th.wikipedia.org/wiki/%E0%B8%97%E0%B8%A4%E0%B8%A9%E0%B8%8E%E0%B8%B5%E0%B9%80%E0%B8%81%E0%B8%A1" title="ทฤษฎีเกม – Thai" lang="th" hreflang="th" data-title="ทฤษฎีเกม" data-language-autonym="ไทย" data-language-local-name="Thai" class="interlanguage-link-target"><span>ไทย</span></a></li><li class="interlanguage-link interwiki-tr mw-list-item"><a href="https://tr.wikipedia.org/wiki/Oyun_teorisi" title="Oyun teorisi – Turkish" lang="tr" hreflang="tr" data-title="Oyun teorisi" data-language-autonym="Türkçe" data-language-local-name="Turkish" class="interlanguage-link-target"><span>Türkçe</span></a></li><li class="interlanguage-link interwiki-uk mw-list-item"><a href="https://uk.wikipedia.org/wiki/%D0%A2%D0%B5%D0%BE%D1%80%D1%96%D1%8F_%D1%96%D0%B3%D0%BE%D1%80" title="Теорія ігор – Ukrainian" lang="uk" hreflang="uk" data-title="Теорія ігор" data-language-autonym="Українська" data-language-local-name="Ukrainian" class="interlanguage-link-target"><span>Українська</span></a></li><li class="interlanguage-link interwiki-ur mw-list-item"><a href="https://ur.wikipedia.org/wiki/%D9%86%D8%B8%D8%B1%DB%8C%DB%81_%D8%A8%D8%A7%D8%B2%DB%8C" title="نظریہ بازی – Urdu" lang="ur" hreflang="ur" data-title="نظریہ بازی" data-language-autonym="اردو" data-language-local-name="Urdu" class="interlanguage-link-target"><span>اردو</span></a></li><li class="interlanguage-link interwiki-ug mw-list-item"><a href="https://ug.wikipedia.org/wiki/%D8%A6%D9%88%D9%8A%DB%87%D9%86_%D9%86%DB%95%D8%B2%DB%95%D8%B1%D9%89%D9%8A%DB%95%D8%B3%D9%89" title="ئويۇن نەزەرىيەسى – Uyghur" lang="ug" hreflang="ug" data-title="ئويۇن نەزەرىيەسى" data-language-autonym="ئۇيغۇرچە / Uyghurche" data-language-local-name="Uyghur" class="interlanguage-link-target"><span>ئۇيغۇرچە / Uyghurche</span></a></li><li class="interlanguage-link interwiki-vi mw-list-item"><a href="https://vi.wikipedia.org/wiki/L%C3%BD_thuy%E1%BA%BFt_tr%C3%B2_ch%C6%A1i" title="Lý thuyết trò chơi – Vietnamese" lang="vi" hreflang="vi" data-title="Lý thuyết trò chơi" data-language-autonym="Tiếng Việt" data-language-local-name="Vietnamese" class="interlanguage-link-target"><span>Tiếng Việt</span></a></li><li class="interlanguage-link interwiki-fiu-vro mw-list-item"><a href="https://fiu-vro.wikipedia.org/wiki/M%C3%A4ngoteooria" title="Mängoteooria – Võro" lang="vro" hreflang="vro" data-title="Mängoteooria" data-language-autonym="Võro" data-language-local-name="Võro" class="interlanguage-link-target"><span>Võro</span></a></li><li class="interlanguage-link interwiki-war mw-list-item"><a href="https://war.wikipedia.org/wiki/Teyorya_hin_mulay" title="Teyorya hin mulay – Waray" lang="war" hreflang="war" data-title="Teyorya hin mulay" data-language-autonym="Winaray" data-language-local-name="Waray" class="interlanguage-link-target"><span>Winaray</span></a></li><li class="interlanguage-link interwiki-wuu mw-list-item"><a href="https://wuu.wikipedia.org/wiki/%E5%8D%9A%E5%BC%88%E8%AE%BA" title="博弈论 – Wu" lang="wuu" hreflang="wuu" data-title="博弈论" data-language-autonym="吴语" data-language-local-name="Wu" class="interlanguage-link-target"><span>吴语</span></a></li><li class="interlanguage-link interwiki-yi mw-list-item"><a href="https://yi.wikipedia.org/wiki/%D7%A9%D7%A4%D7%99%D7%9C_%D7%98%D7%A2%D7%90%D7%A8%D7%99%D7%A2" title="שפיל טעאריע – Yiddish" lang="yi" hreflang="yi" data-title="שפיל טעאריע" data-language-autonym="ייִדיש" data-language-local-name="Yiddish" class="interlanguage-link-target"><span>ייִדיש</span></a></li><li class="interlanguage-link interwiki-zh-yue mw-list-item"><a href="https://zh-yue.wikipedia.org/wiki/%E5%8D%9A%E5%BC%88%E8%AB%96" title="博弈論 – Cantonese" lang="yue" hreflang="yue" data-title="博弈論" data-language-autonym="粵語" data-language-local-name="Cantonese" class="interlanguage-link-target"><span>粵語</span></a></li><li class="interlanguage-link interwiki-zh mw-list-item"><a href="https://zh.wikipedia.org/wiki/%E5%8D%9A%E5%BC%88%E8%AE%BA" title="博弈论 – Chinese" lang="zh" hreflang="zh" data-title="博弈论" data-language-autonym="中文" data-language-local-name="Chinese" class="interlanguage-link-target"><span>中文</span></a></li> </ul> <div class="after-portlet after-portlet-lang"><span class="wb-langlinks-edit wb-langlinks-link"><a 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id="siteSub" class="noprint">From Wikipedia, the free encyclopedia</div> </div> <div id="contentSub"><div id="mw-content-subtitle"></div></div> <div id="mw-content-text" class="mw-body-content"><div class="mw-content-ltr mw-parser-output" lang="en" dir="ltr"><div class="shortdescription nomobile noexcerpt noprint searchaux" style="display:none">Mathematical models of strategic interactions</div> <style data-mw-deduplicate="TemplateStyles:r1236090951">.mw-parser-output .hatnote{font-style:italic}.mw-parser-output div.hatnote{padding-left:1.6em;margin-bottom:0.5em}.mw-parser-output .hatnote i{font-style:normal}.mw-parser-output .hatnote+link+.hatnote{margin-top:-0.5em}@media print{body.ns-0 .mw-parser-output .hatnote{display:none!important}}</style><div role="note" class="hatnote navigation-not-searchable">This article is about the mathematical study of strategic behavior. For the mathematical study of sequential games, see <a href="/wiki/Combinatorial_game_theory" title="Combinatorial game theory">Combinatorial game theory</a>. For the study of playing games for entertainment, see <a href="/wiki/Game_studies" title="Game studies">Game studies</a>. For the YouTube series, see <a href="/wiki/MatPat" title="MatPat">MatPat</a>. 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title="Cultural economics">Cultural</a></li> <li><a href="/wiki/Democracy_and_economic_growth" title="Democracy and economic growth">Democracy</a></li> <li><a href="/wiki/Demographic_economics" title="Demographic economics">Demographic</a></li> <li><a href="/wiki/Development_economics" title="Development economics">Development</a></li> <li><a href="/wiki/Economics_of_digitization" title="Economics of digitization">Digitization</a></li> <li><a href="/wiki/Ecological_economics" title="Ecological economics">Ecological</a></li> <li><a href="/wiki/Education_economics" title="Education economics">Education</a></li> <li><a href="/wiki/Engineering_economics" title="Engineering economics">Engineering</a></li> <li><a href="/wiki/Environmental_economics" title="Environmental economics">Environmental</a></li> <li><a href="/wiki/Evolutionary_economics" title="Evolutionary economics">Evolutionary</a></li> <li><a href="/wiki/Expeditionary_economics" title="Expeditionary economics">Expeditionary</a></li> <li><a href="/wiki/Feminist_economics" title="Feminist economics">Feminist</a></li> <li><a href="/wiki/Financial_economics" title="Financial economics">Financial</a></li> <li><a href="/wiki/Economic_geography" title="Economic geography">Geographical</a></li> <li><a href="/wiki/Happiness_economics" title="Happiness economics">Happiness</a></li> <li><a href="/wiki/Health_economics" title="Health economics">Health</a></li> <li><a href="/wiki/Economic_history" title="Economic history">Historical</a></li> <li><a href="/wiki/Humanistic_economics" title="Humanistic economics">Humanistic</a></li> <li><a href="/wiki/Industrial_organization" title="Industrial organization">Industrial organization</a></li> <li><a href="/wiki/Information_economics" title="Information economics">Information</a></li> <li><a href="/wiki/Institutional_economics" title="Institutional economics">Institutional</a></li> <li><a href="/wiki/Knowledge_economy" title="Knowledge 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<li><a href="/wiki/Public_choice" title="Public choice">Public choice</a> / <a href="/wiki/Social_choice_theory" title="Social choice theory">Social choice theory</a></li> <li><a href="/wiki/Regional_economics" title="Regional economics">Regional</a></li> <li><a href="/wiki/Rural_economics" title="Rural economics">Rural</a></li> <li><a href="/wiki/Service_economy" title="Service economy">Service</a></li> <li><a href="/wiki/Socioeconomics" class="mw-redirect" title="Socioeconomics">Socio</a></li> <li><a href="/wiki/Economic_sociology" title="Economic sociology">Sociological</a></li> <li><a href="/wiki/Solidarity_economy" title="Solidarity economy">Solidarity</a></li> <li><a href="/wiki/Economic_statistics" title="Economic statistics">Statistics</a></li> <li><a href="/wiki/Urban_economics" title="Urban economics">Urban</a></li> <li><a href="/wiki/Welfare_economics" title="Welfare economics">Welfare</a></li></ul></div></div></td> </tr><tr><td class="sidebar-content"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="background:#efefef;;color: var(--color-base)">Notable <a href="/wiki/Economist" title="Economist">economists</a></div><div class="sidebar-list-content mw-collapsible-content"> <div class="excerpt-block"><div class="excerpt"> <ul><li><a href="/wiki/Bernard_de_Mandeville" class="mw-redirect" title="Bernard de Mandeville">de Mandeville</a></li> <li><a href="/wiki/Fran%C3%A7ois_Quesnay" title="François Quesnay">Quesnay</a></li> <li><a href="/wiki/Adam_Smith" title="Adam Smith">Smith</a></li> <li><a href="/wiki/Thomas_Robert_Malthus" title="Thomas Robert Malthus">Malthus</a></li> <li><a href="/wiki/Jean-Baptiste_Say" title="Jean-Baptiste Say">Say</a></li> <li><a href="/wiki/David_Ricardo" title="David Ricardo">Ricardo</a></li> <li><a href="/wiki/Johann_Heinrich_von_Th%C3%BCnen" title="Johann Heinrich von Thünen">von Thünen</a></li> <li><a href="/wiki/Friedrich_List" title="Friedrich List">List</a></li> <li><a href="/wiki/Fr%C3%A9d%C3%A9ric_Bastiat" title="Frédéric Bastiat">Bastiat</a></li> <li><a href="/wiki/Antoine_Augustin_Cournot" title="Antoine Augustin Cournot">Cournot</a></li> <li><a href="/wiki/John_Stuart_Mill" title="John Stuart Mill">Mill</a></li> <li><a href="/wiki/Hermann_Heinrich_Gossen" title="Hermann Heinrich Gossen">Gossen</a></li> <li><a href="/wiki/Karl_Marx" title="Karl Marx">Marx</a></li> <li><a href="/wiki/L%C3%A9on_Walras" title="Léon Walras">Walras</a></li> <li><a href="/wiki/William_Stanley_Jevons" title="William Stanley Jevons">Jevons</a></li> <li><a href="/wiki/Henry_George" title="Henry George">George</a></li> <li><a href="/wiki/Carl_Menger" title="Carl Menger">Menger</a></li> <li><a href="/wiki/Alfred_Marshall" title="Alfred Marshall">Marshall</a></li> <li><a href="/wiki/Francis_Ysidro_Edgeworth" title="Francis Ysidro Edgeworth">Edgeworth</a></li> <li><a href="/wiki/John_Bates_Clark" title="John Bates Clark">Clark</a></li> <li><a href="/wiki/Vilfredo_Pareto" title="Vilfredo Pareto">Pareto</a></li> <li><a href="/wiki/Eugen_von_B%C3%B6hm-Bawerk" title="Eugen von Böhm-Bawerk">von Böhm-Bawerk</a></li> <li><a href="/wiki/Friedrich_von_Wieser" title="Friedrich von Wieser">von Wieser</a></li> <li><a href="/wiki/Thorstein_Veblen" title="Thorstein Veblen">Veblen</a></li> <li><a href="/wiki/Irving_Fisher" title="Irving Fisher">Fisher</a></li> <li><a href="/wiki/Arthur_Cecil_Pigou" title="Arthur Cecil Pigou">Pigou</a></li> <li><a href="/wiki/Eli_Heckscher" title="Eli Heckscher">Heckscher</a></li> <li><a href="/wiki/Ludwig_von_Mises" title="Ludwig von Mises">von Mises</a></li> <li><a href="/wiki/Joseph_Schumpeter" title="Joseph Schumpeter">Schumpeter</a></li> <li><a href="/wiki/John_Maynard_Keynes" title="John Maynard Keynes">Keynes</a></li> <li><a href="/wiki/Frank_Knight" title="Frank Knight">Knight</a></li> <li><a href="/wiki/Karl_Polanyi" title="Karl Polanyi">Polanyi</a></li> <li><a href="/wiki/Ragnar_Frisch" title="Ragnar Frisch">Frisch</a></li> <li><a href="/wiki/Piero_Sraffa" title="Piero Sraffa">Sraffa</a></li> <li><a href="/wiki/Gunnar_Myrdal" title="Gunnar Myrdal">Myrdal</a></li> <li><a href="/wiki/Friedrich_Hayek" title="Friedrich Hayek">Hayek</a></li> <li><a href="/wiki/Micha%C5%82_Kalecki" title="Michał Kalecki">Kalecki</a></li> <li><a href="/wiki/Wilhelm_R%C3%B6pke" title="Wilhelm Röpke">Röpke</a></li> <li><a href="/wiki/Simon_Kuznets" title="Simon Kuznets">Kuznets</a></li> <li><a href="/wiki/Jan_Tinbergen" title="Jan Tinbergen">Tinbergen</a></li> <li><a href="/wiki/Joan_Robinson" title="Joan Robinson">Robinson</a></li> <li><a href="/wiki/John_von_Neumann" title="John von Neumann">von Neumann</a></li> <li><a href="/wiki/John_Hicks" title="John Hicks">Hicks</a></li> <li><a href="/wiki/Oskar_R._Lange" title="Oskar R. Lange">Lange</a></li> <li><a href="/wiki/Wassily_Leontief" title="Wassily Leontief">Leontief</a></li> <li><a href="/wiki/John_Kenneth_Galbraith" title="John Kenneth Galbraith">Galbraith</a></li> <li><a href="/wiki/Tjalling_Koopmans" title="Tjalling Koopmans">Koopmans</a></li> <li><a href="/wiki/E._F._Schumacher" title="E. F. Schumacher">Schumacher</a></li> <li><a href="/wiki/Milton_Friedman" title="Milton Friedman">Friedman</a></li> <li><a href="/wiki/Paul_Samuelson" title="Paul Samuelson">Samuelson</a></li> <li><a href="/wiki/Herbert_A._Simon" title="Herbert A. Simon">Simon</a></li> <li><a href="/wiki/James_M._Buchanan" title="James M. Buchanan">Buchanan</a></li> <li><a href="/wiki/Kenneth_Arrow" title="Kenneth Arrow">Arrow</a></li> <li><a href="/wiki/William_Baumol" title="William Baumol">Baumol</a></li> <li><a href="/wiki/Robert_Solow" title="Robert Solow">Solow</a></li> <li><a href="/wiki/Murray_Rothbard" title="Murray Rothbard">Rothbard</a></li> <li><a href="/wiki/Alan_Greenspan" title="Alan Greenspan">Greenspan</a></li> <li><a href="/wiki/Thomas_Sowell" title="Thomas Sowell">Sowell</a></li> <li><a href="/wiki/Gary_Becker" title="Gary Becker">Becker</a></li> <li><a href="/wiki/Elinor_Ostrom" title="Elinor Ostrom">Ostrom</a></li> <li><a href="/wiki/Amartya_Sen" title="Amartya Sen">Sen</a></li> <li><a href="/wiki/Robert_Lucas_Jr." title="Robert Lucas Jr.">Lucas</a></li> <li><a href="/wiki/Joseph_Stiglitz" title="Joseph Stiglitz">Stiglitz</a></li> <li><a href="/wiki/Richard_Thaler" title="Richard Thaler">Thaler</a></li> <li><a href="/wiki/Hans-Hermann_Hoppe" title="Hans-Hermann Hoppe">Hoppe</a></li> <li><a href="/wiki/Paul_Krugman" title="Paul Krugman">Krugman</a></li> <li><a href="/wiki/Thomas_Piketty" title="Thomas Piketty">Piketty</a></li> <li><i><a href="/wiki/Category:Economists" title="Category:Economists">more</a></i></li></ul></div></div> </div></div></td> </tr><tr><td class="sidebar-content"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="background:#efefef;;color: var(--color-base)"><a href="/wiki/Category:Economics_lists" title="Category:Economics lists">Lists</a></div><div class="sidebar-list-content mw-collapsible-content"> <ul><li><a href="/wiki/Glossary_of_economics" title="Glossary of economics">Glossary</a></li> <li><a href="/wiki/List_of_economists" title="List of economists">Economists</a></li> <li><a href="/wiki/List_of_important_publications_in_economics" title="List of important publications in economics">Publications</a> (<a href="/wiki/List_of_economics_journals" title="List of economics journals">journals</a>)</li> <li><a href="/wiki/Schools_of_economic_thought" title="Schools of economic thought">Schools</a></li></ul> </div></div></td> </tr><tr><td class="sidebar-below"> <ul><li><span class="nowrap"><span class="noviewer" typeof="mw:File"><a href="/wiki/File:Emblem-money.svg" class="mw-file-description"><img alt="icon" src="//upload.wikimedia.org/wikipedia/commons/thumb/f/f3/Emblem-money.svg/16px-Emblem-money.svg.png" decoding="async" width="16" height="16" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/f/f3/Emblem-money.svg/24px-Emblem-money.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/f/f3/Emblem-money.svg/32px-Emblem-money.svg.png 2x" data-file-width="48" data-file-height="48" /></a></span> </span><a href="/wiki/Portal:Business" title="Portal:Business">Business portal</a></li> <li><span class="nowrap"><span class="noviewer" typeof="mw:File"><span><img alt="icon" 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plainlist"><tbody><tr><td class="sidebar-pretitle">Part of <a href="/wiki/Category:Strategy" title="Category:Strategy">a series</a> on</td></tr><tr><th class="sidebar-title-with-pretitle"><a href="/wiki/Strategy" title="Strategy">Strategy</a></th></tr><tr><td class="sidebar-image"><span typeof="mw:File"><a href="/wiki/File:Strategy_Concept.svg" class="mw-file-description" title="Strategy topics"><img alt="Strategy topics" src="//upload.wikimedia.org/wikipedia/commons/thumb/6/68/Strategy_Concept.svg/80px-Strategy_Concept.svg.png" decoding="async" width="80" height="80" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/68/Strategy_Concept.svg/120px-Strategy_Concept.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/68/Strategy_Concept.svg/160px-Strategy_Concept.svg.png 2x" data-file-width="455" data-file-height="455" /></a></span></td></tr><tr><td class="sidebar-content"> <div class="sidebar-list mw-collapsible"><div class="sidebar-list-title" style="background:#DDFFDD;;color: var(--color-base)">Analysis methods</div><div class="sidebar-list-content mw-collapsible-content"> <ul><li><a href="/wiki/Strategy" title="Strategy">Strategy</a> •  <a href="/wiki/Strategic_management" title="Strategic management">Strategic management</a></li> <li><a href="/wiki/Military_strategy" title="Military strategy">Military strategy</a> •  <a href="/wiki/Strategic_studies" title="Strategic studies">Strategic studies</a></li> <li><a href="/wiki/Strategic_planning" title="Strategic planning">Strategic planning</a> •  <a href="/wiki/Strategic_thinking" title="Strategic thinking">Strategic thinking</a></li> <li><a href="/wiki/Decision_theory" title="Decision theory">Decision theory</a> •  <a class="mw-selflink selflink">Game theory</a></li></ul></div></div></td> </tr><tr><td class="sidebar-content"> <div class="sidebar-list mw-collapsible"><div class="sidebar-list-title" style="background:#DDFFDD;;color: var(--color-base)">Major thinkers</div><div class="sidebar-list-content mw-collapsible-content"> <ul><li><a href="/wiki/Michael_Porter" title="Michael Porter">Michael Porter</a>  •  <a href="/wiki/Rita_Gunther_McGrath" title="Rita Gunther McGrath">Rita Gunther McGrath</a></li> <li><a href="/wiki/Bruce_Henderson" title="Bruce Henderson">Bruce Henderson</a>  •  <a href="/wiki/Gary_Hamel" title="Gary Hamel">Gary Hamel</a></li> <li><a href="/wiki/Candace_A._Yano" title="Candace A. Yano">Candace A. Yano</a>  •  <a href="/wiki/C._K._Prahalad" title="C. K. Prahalad">C. K. Prahalad</a></li> <li><a href="/wiki/James_C._Collins" title="James C. Collins">Jim Collins</a>  •  <a href="/wiki/B._H._Liddell_Hart" title="B. H. Liddell Hart">Liddell Hart</a></li> <li><a href="/wiki/Carl_von_Clausewitz" title="Carl von Clausewitz">Carl von Clausewitz</a>  •  <a href="/wiki/Sun_Tzu" title="Sun Tzu">Sun Tzu</a></li> <li><a href="/wiki/Julian_Corbett" title="Julian Corbett">Julian Corbett</a>  •  <a href="/wiki/Alfred_Thayer_Mahan" title="Alfred Thayer Mahan">Alfred Thayer Mahan</a></li> <li><a href="/wiki/J.C._Wylie" title="J.C. Wylie">J.C. Wylie</a>  •  <a href="/wiki/Adrian_Slywotzky" title="Adrian Slywotzky">Adrian Slywotzky</a></li> <li><a href="/wiki/Sharon_Oster" title="Sharon Oster">Sharon Oster</a>  •  <a href="/wiki/Chris_Zook" title="Chris Zook">Chris Zook</a></li> <li><a href="/wiki/Henry_Mintzberg" title="Henry Mintzberg">Henry Mintzberg</a></li></ul></div></div></td> </tr><tr><td class="sidebar-content"> <div class="sidebar-list mw-collapsible"><div class="sidebar-list-title" style="background:#DDFFDD;;color: var(--color-base)">Concepts</div><div class="sidebar-list-content mw-collapsible-content"> <ul><li><a href="/wiki/Business_model" title="Business model">Business model</a>  •  <a href="/wiki/Competitive_advantage" title="Competitive advantage">Competitive advantage</a></li> <li><a href="/wiki/Value_chain" title="Value chain">Value chain</a>  •  <a href="/wiki/Performance_effects" title="Performance effects">Performance effects</a></li> <li><a href="/wiki/Core_competency" title="Core competency">Core competency</a> •  <a href="/wiki/Porter%27s_generic_strategies" title="Porter's generic strategies">Generic strategies</a></li> <li><a href="/wiki/Mission_statement" title="Mission statement">Mission statement</a></li></ul></div></div></td> </tr><tr><td class="sidebar-content"> <div class="sidebar-list mw-collapsible"><div class="sidebar-list-title" style="background:#DDFFDD;;color: var(--color-base)">Frameworks and tools</div><div class="sidebar-list-content mw-collapsible-content"> <ul><li><a href="/wiki/SWOT_analysis" title="SWOT analysis">SWOT</a> • <a href="/wiki/Porter%27s_five_forces_analysis" title="Porter's five forces analysis">Five forces</a></li> <li><a href="/wiki/Balanced_scorecard" title="Balanced scorecard">Balanced scorecard</a> • <a href="/wiki/Ansoff_matrix" title="Ansoff matrix">Ansoff matrix</a></li> <li><a href="/wiki/OGSM" title="OGSM">OGSM</a> • <a href="/wiki/Managerial_grid_model" title="Managerial grid model">Managerial grid model</a></li> <li><a href="/wiki/PEST_analysis" title="PEST analysis">PEST analysis</a> • <a href="/wiki/Growth%E2%80%93share_matrix" title="Growth–share matrix">Growth–share matrix</a></li> <li><a href="/wiki/Segmenting-targeting-positioning" title="Segmenting-targeting-positioning">STP</a> • <a href="/wiki/MECE_principle" title="MECE principle">MECE principle</a></li> <li><a href="/wiki/Business_Model_Canvas" title="Business Model Canvas">Business Model Canvas</a> • <a href="/wiki/Kraljic_matrix" title="Kraljic matrix">Kraljic matrix</a></li> <li><a href="/wiki/Strategic_Grid_Model" class="mw-redirect" title="Strategic Grid Model">Strategic Grid Model</a> • <a href="/wiki/Strategy_map" title="Strategy map">Strategy map</a> • <a href="/wiki/VRIO" title="VRIO">VRIO</a></li></ul></div></div></td> </tr><tr><td class="sidebar-navbar"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1239400231"><div class="navbar plainlinks hlist navbar-mini"><ul><li class="nv-view"><a href="/wiki/Template:Strategy" title="Template:Strategy"><abbr title="View this template">v</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:Strategy" title="Template talk:Strategy"><abbr title="Discuss this template">t</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:EditPage/Template:Strategy" title="Special:EditPage/Template:Strategy"><abbr title="Edit this template">e</abbr></a></li></ul></div></td></tr></tbody></table> <p><b>Game theory</b> is the study of <a href="/wiki/Mathematical_model" title="Mathematical model">mathematical models</a> of strategic interactions.<sup id="cite_ref-Myerson_1-0" class="reference"><a href="#cite_note-Myerson-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> It has applications in many fields of <a href="/wiki/Social_science" title="Social science">social science</a>, and is used extensively in <a href="/wiki/Economics" title="Economics">economics</a>, <a href="/wiki/Logic" title="Logic">logic</a>, <a href="/wiki/Systems_science" title="Systems science">systems science</a> and <a href="/wiki/Computer_science" title="Computer science">computer science</a>.<sup id="cite_ref-2" class="reference"><a href="#cite_note-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> Initially, game theory addressed two-person <a href="/wiki/Zero-sum_game" title="Zero-sum game">zero-sum games</a>, in which a participant's gains or losses are exactly balanced by the losses and gains of the other participant. In the 1950s, it was extended to the study of non zero-sum games, and was eventually applied to a wide range of <a href="/wiki/Human_behavior" title="Human behavior">behavioral relations</a>. It is now an <a href="/wiki/Umbrella_term" class="mw-redirect" title="Umbrella term">umbrella term</a> for the <a href="/wiki/Science" title="Science">science</a> of rational <a href="/wiki/Decision-making" title="Decision-making">decision making</a> in humans, animals, and computers. </p><p>Modern game theory began with the idea of mixed-strategy equilibria in two-person zero-sum games and its proof by <a href="/wiki/John_von_Neumann" title="John von Neumann">John von Neumann</a>. Von Neumann's original proof used the <a href="/wiki/Brouwer_fixed-point_theorem" title="Brouwer fixed-point theorem">Brouwer fixed-point theorem</a> on continuous mappings into compact <a href="/wiki/Convex_set" title="Convex set">convex sets</a>, which became a standard method in game theory and <a href="/wiki/Mathematical_economics" title="Mathematical economics">mathematical economics</a>. His paper was followed by <i><a href="/wiki/Theory_of_Games_and_Economic_Behavior" title="Theory of Games and Economic Behavior">Theory of Games and Economic Behavior</a></i> (1944), co-written with <a href="/wiki/Oskar_Morgenstern" title="Oskar Morgenstern">Oskar Morgenstern</a>, which considered <a href="/wiki/Cooperative_game_theory" title="Cooperative game theory">cooperative games</a> of several players.<sup id="cite_ref-3" class="reference"><a href="#cite_note-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> The second edition provided an <a href="/wiki/Von_Neumann%E2%80%93Morgenstern_utility_theorem" title="Von Neumann–Morgenstern utility theorem">axiomatic theory</a> of <a href="/wiki/Expected_utility_hypothesis" title="Expected utility hypothesis">expected utility</a>, which allowed mathematical statisticians and economists to treat decision-making under uncertainty.<sup id="cite_ref-4" class="reference"><a href="#cite_note-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> </p><p>Game theory was developed extensively in the 1950s, and was explicitly applied to <a href="/wiki/Evolution" title="Evolution">evolution</a> in the 1970s, although similar developments go back at least as far as the 1930s. Game theory has been widely recognized as an important tool in many fields. <a href="/wiki/John_Maynard_Smith" title="John Maynard Smith">John Maynard Smith</a> was awarded the <a href="/wiki/Crafoord_Prize" title="Crafoord Prize">Crafoord Prize</a> for his application of <a href="/wiki/Evolutionary_game_theory" title="Evolutionary game theory">evolutionary game theory</a> in 1999, and fifteen game theorists have won the <a href="/wiki/Nobel_Memorial_Prize_in_Economic_Sciences" title="Nobel Memorial Prize in Economic Sciences">Nobel Prize in economics</a> as of 2020, including most recently <a href="/wiki/Paul_Milgrom" title="Paul Milgrom">Paul Milgrom</a> and <a href="/wiki/Robert_B._Wilson" title="Robert B. Wilson">Robert B. Wilson</a>. </p> <style data-mw-deduplicate="TemplateStyles:r886046785">.mw-parser-output .toclimit-2 .toclevel-1 ul,.mw-parser-output .toclimit-3 .toclevel-2 ul,.mw-parser-output .toclimit-4 .toclevel-3 ul,.mw-parser-output .toclimit-5 .toclevel-4 ul,.mw-parser-output .toclimit-6 .toclevel-5 ul,.mw-parser-output .toclimit-7 .toclevel-6 ul{display:none}</style><div class="toclimit-3"><meta property="mw:PageProp/toc" /></div> <div class="mw-heading mw-heading2"><h2 id="History">History</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Game_theory&action=edit&section=1" title="Edit section: History"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="Earliest_results">Earliest results</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Game_theory&action=edit&section=2" title="Edit section: Earliest results"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>In 1713, a letter attributed to Charles Waldegrave, an active <a href="/wiki/Jacobitism" title="Jacobitism">Jacobite</a> and uncle to British diplomat <a href="/wiki/James_Waldegrave,_1st_Earl_Waldegrave" title="James Waldegrave, 1st Earl Waldegrave">James Waldegrave</a>, analyzed a game called "<a href="/wiki/Le_her" title="Le her">le her</a>". Waldegrave provided a <a href="/wiki/Minimax" title="Minimax">minimax</a> <a href="/wiki/Mixed_strategy" class="mw-redirect" title="Mixed strategy">mixed strategy</a> solution to a two-person version of the card game, and the problem is now known as the <a href="/wiki/Waldegrave_problem" title="Waldegrave problem">Waldegrave problem</a>.<sup id="cite_ref-GT-PD-01_5-0" class="reference"><a href="#cite_note-GT-PD-01-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-6" class="reference"><a href="#cite_note-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup> </p><p>In 1838, <a href="/wiki/Antoine_Augustin_Cournot" title="Antoine Augustin Cournot">Antoine Augustin Cournot</a> provided a <a href="/wiki/Cournot_competition" title="Cournot competition">model of competition</a> in <a href="/wiki/Oligopoly" title="Oligopoly">oligopolies</a>. Though he did not refer to it as such, he presented a solution that is the <a href="/wiki/Nash_equilibrium" title="Nash equilibrium">Nash equilibrium</a> of the game in his <span title="French-language text"><i lang="fr">Recherches sur les principes mathématiques de la théorie des richesses</i></span> (<i>Researches into the Mathematical Principles of the Theory of Wealth</i>). In 1883, <a href="/wiki/Joseph_Bertrand" title="Joseph Bertrand">Joseph Bertrand</a> critiqued Cournot's model as unrealistic, providing an alternative model of price competition<sup id="cite_ref-:42_7-0" class="reference"><a href="#cite_note-:42-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup> which would later be formalized by <a href="/wiki/Francis_Ysidro_Edgeworth" title="Francis Ysidro Edgeworth">Francis Ysidro Edgeworth</a>.<sup id="cite_ref-8" class="reference"><a href="#cite_note-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup> </p><p>In 1913, <a href="/wiki/Ernst_Zermelo" title="Ernst Zermelo">Ernst Zermelo</a> published <span title="German-language text"><i lang="de">Über eine Anwendung der Mengenlehre auf die Theorie des Schachspiels</i></span> (<i>On an Application of Set Theory to the Theory of the Game of Chess</i>), which proved that the optimal chess strategy is <a href="/wiki/Strictly_determined_game" title="Strictly determined game">strictly determined</a>.<sup id="cite_ref-9" class="reference"><a href="#cite_note-9"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Foundation">Foundation</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Game_theory&action=edit&section=3" title="Edit section: Foundation"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:JohnvonNeumann-LosAlamos.gif" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/5/5e/JohnvonNeumann-LosAlamos.gif/170px-JohnvonNeumann-LosAlamos.gif" decoding="async" width="170" height="222" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/5/5e/JohnvonNeumann-LosAlamos.gif/255px-JohnvonNeumann-LosAlamos.gif 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/5/5e/JohnvonNeumann-LosAlamos.gif/340px-JohnvonNeumann-LosAlamos.gif 2x" data-file-width="490" data-file-height="639" /></a><figcaption><a href="/wiki/John_von_Neumann" title="John von Neumann">John von Neumann</a></figcaption></figure> <p>The work of <a href="/wiki/John_von_Neumann" title="John von Neumann">John von Neumann</a> established game theory as its own independent field in the early-to-mid 20th century, with von Neumann publishing his paper <i>On the Theory of Games of Strategy</i> in 1928.<sup id="cite_ref-10" class="reference"><a href="#cite_note-10"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-11" class="reference"><a href="#cite_note-11"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup> Von Neumann's original proof used <a href="/wiki/Brouwer%27s_fixed-point_theorem" class="mw-redirect" title="Brouwer's fixed-point theorem">Brouwer's fixed-point theorem</a> on continuous <a href="/wiki/Map_(mathematics)" title="Map (mathematics)">mappings</a> into compact <a href="/wiki/Convex_set" title="Convex set">convex sets</a>, which became a standard method in game theory and <a href="/wiki/Mathematical_economics" title="Mathematical economics">mathematical economics</a>. Von Neumann's work in game theory culminated in his 1944 book <i><a href="/wiki/Theory_of_Games_and_Economic_Behavior" title="Theory of Games and Economic Behavior">Theory of Games and Economic Behavior</a></i>, co-authored with <a href="/wiki/Oskar_Morgenstern" title="Oskar Morgenstern">Oskar Morgenstern</a>.<sup id="cite_ref-12" class="reference"><a href="#cite_note-12"><span class="cite-bracket">[</span>12<span class="cite-bracket">]</span></a></sup> The second edition of this book provided an <a href="/wiki/Axiomatic_set_theory" class="mw-redirect" title="Axiomatic set theory">axiomatic theory of utility</a>, which reincarnated <a href="/wiki/Daniel_Bernoulli" title="Daniel Bernoulli">Daniel Bernoulli's</a> old theory of utility (of money) as an independent discipline. This foundational work contains the method for finding mutually consistent solutions for two-person zero-sum games. Subsequent work focused primarily on <a href="/wiki/Cooperative_game_theory" title="Cooperative game theory">cooperative game</a> theory, which analyzes optimal strategies for groups of individuals, presuming that they can enforce agreements between them about proper strategies.<sup id="cite_ref-13" class="reference"><a href="#cite_note-13"><span class="cite-bracket">[</span>13<span class="cite-bracket">]</span></a></sup> </p><p>In his 1938 book <span title="French-language text"><i lang="fr">Applications aux Jeux de Hasard</i></span> and earlier notes, <a href="/wiki/%C3%89mile_Borel" title="Émile Borel">Émile Borel</a> proved a <a href="/wiki/Minimax_theorem" title="Minimax theorem">minimax theorem</a> for two-person zero-sum matrix games only when the pay-off matrix is symmetric and provided a solution to a non-trivial infinite game (known in English as <a href="/wiki/Blotto_game" title="Blotto game">Blotto game</a>). Borel conjectured the non-existence of mixed-strategy equilibria in <a href="/wiki/Finite_Game" class="mw-redirect" title="Finite Game">finite two-person zero-sum games</a>, a conjecture that was proved false by von Neumann.<sup id="cite_ref-14" class="reference"><a href="#cite_note-14"><span class="cite-bracket">[</span>14<span class="cite-bracket">]</span></a></sup> </p> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:John_f_nash_20061102_3.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/9/91/John_f_nash_20061102_3.jpg/170px-John_f_nash_20061102_3.jpg" decoding="async" width="170" height="214" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/9/91/John_f_nash_20061102_3.jpg/255px-John_f_nash_20061102_3.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/9/91/John_f_nash_20061102_3.jpg/340px-John_f_nash_20061102_3.jpg 2x" data-file-width="715" data-file-height="901" /></a><figcaption><a href="/wiki/John_Forbes_Nash_Jr." title="John Forbes Nash Jr.">John Nash</a></figcaption></figure> <p>In 1950, <a href="/wiki/John_Forbes_Nash" class="mw-redirect" title="John Forbes Nash">John Nash</a> developed a criterion for mutual consistency of players' strategies known as the <a href="/wiki/Nash_equilibrium" title="Nash equilibrium">Nash equilibrium</a>, applicable to a wider variety of games than the criterion proposed by von Neumann and Morgenstern. Nash proved that every finite n-player, non-zero-sum (not just two-player zero-sum) <a href="/wiki/Non-cooperative_game" class="mw-redirect" title="Non-cooperative game">non-cooperative game</a> has what is now known as a Nash equilibrium in mixed strategies. </p><p>Game theory experienced a flurry of activity in the 1950s, during which the concepts of the <a href="/wiki/Core_(economics)" class="mw-redirect" title="Core (economics)">core</a>, the <a href="/wiki/Extensive_form_game" class="mw-redirect" title="Extensive form game">extensive form game</a>, <a href="/wiki/Fictitious_play" title="Fictitious play">fictitious play</a>, <a href="/wiki/Repeated_game" title="Repeated game">repeated games</a>, and the <a href="/wiki/Shapley_value" title="Shapley value">Shapley value</a> were developed. The 1950s also saw the first applications of game theory to <a href="/wiki/Philosophy" title="Philosophy">philosophy</a> and <a href="/wiki/Political_science" title="Political science">political science</a>. The first mathematical discussion of the <a href="/wiki/Prisoner%27s_dilemma" title="Prisoner's dilemma">prisoner's dilemma</a> appeared, and an experiment was undertaken by mathematicians <a href="/wiki/Merrill_M._Flood" title="Merrill M. Flood">Merrill M. Flood</a> and <a href="/wiki/Melvin_Dresher" title="Melvin Dresher">Melvin Dresher</a>, as part of the <a href="/wiki/RAND_Corporation" title="RAND Corporation">RAND Corporation</a>'s investigations into game theory. RAND pursued the studies because of possible applications to global <a href="/wiki/Nuclear_strategy" title="Nuclear strategy">nuclear strategy</a>.<sup id="cite_ref-stanfordprisoner_15-0" class="reference"><a href="#cite_note-stanfordprisoner-15"><span class="cite-bracket">[</span>15<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading4"><h4 id="Prize-winning_achievements">Prize-winning achievements</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Game_theory&action=edit&section=4" title="Edit section: Prize-winning achievements"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>In 1965, <a href="/wiki/Reinhard_Selten" title="Reinhard Selten">Reinhard Selten</a> introduced his <a href="/wiki/Solution_concept" title="Solution concept">solution concept</a> of <a href="/wiki/Subgame_perfect_equilibrium" title="Subgame perfect equilibrium">subgame perfect equilibria</a>, which further refined the Nash equilibrium. Later he would introduce <a href="/wiki/Trembling_hand_perfection" class="mw-redirect" title="Trembling hand perfection">trembling hand perfection</a> as well. In 1994 Nash, Selten and <a href="/wiki/John_Harsanyi" title="John Harsanyi">Harsanyi</a> became <a href="/wiki/Nobel_Memorial_Prize_in_Economic_Sciences" title="Nobel Memorial Prize in Economic Sciences">Economics Nobel Laureates</a> for their contributions to economic game theory. </p><p>In the 1970s, game theory was extensively applied in <a href="/wiki/Biology" title="Biology">biology</a>, largely as a result of the work of <a href="/wiki/John_Maynard_Smith" title="John Maynard Smith">John Maynard Smith</a> and his <a href="/wiki/Evolutionarily_stable_strategy" title="Evolutionarily stable strategy">evolutionarily stable strategy</a>. In addition, the concepts of <a href="/wiki/Correlated_equilibrium" title="Correlated equilibrium">correlated equilibrium</a>, <a href="/wiki/Trembling_hand_perfect_equilibrium" title="Trembling hand perfect equilibrium">trembling hand perfection</a> and <a href="/wiki/Common_knowledge_(logic)" title="Common knowledge (logic)">common knowledge</a><sup id="cite_ref-16" class="reference"><a href="#cite_note-16"><span class="cite-bracket">[</span>a<span class="cite-bracket">]</span></a></sup> were introduced and analyzed. </p><p>In 1994, John Nash was awarded the Nobel Memorial Prize in the Economic Sciences for his contribution to game theory. Nash's most famous contribution to game theory is the concept of the Nash equilibrium, which is a solution concept for <a href="/wiki/Non-cooperative_game_theory" title="Non-cooperative game theory">non-cooperative games</a>. A Nash equilibrium is a set of strategies, one for each player, such that no player can improve their payoff by unilaterally changing their strategy. </p><p>In 2005, game theorists <a href="/wiki/Thomas_Schelling" title="Thomas Schelling">Thomas Schelling</a> and <a href="/wiki/Robert_Aumann" title="Robert Aumann">Robert Aumann</a> followed Nash, Selten, and Harsanyi as Nobel Laureates. Schelling worked on dynamic models, early examples of <a href="/wiki/Evolutionary_game_theory" title="Evolutionary game theory">evolutionary game theory</a>. Aumann contributed more to the equilibrium school, introducing equilibrium coarsening and correlated equilibria, and developing an extensive formal analysis of the assumption of common knowledge and of its consequences. </p><p>In 2007, <a href="/wiki/Leonid_Hurwicz" title="Leonid Hurwicz">Leonid Hurwicz</a>, <a href="/wiki/Eric_Maskin" title="Eric Maskin">Eric Maskin</a>, and <a href="/wiki/Roger_Myerson" title="Roger Myerson">Roger Myerson</a> were awarded the Nobel Prize in Economics "for having laid the foundations of <a href="/wiki/Mechanism_design" title="Mechanism design">mechanism design</a> theory". Myerson's contributions include the notion of <a href="/wiki/Proper_equilibrium" title="Proper equilibrium">proper equilibrium</a>, and an important graduate text: <i>Game Theory, Analysis of Conflict</i>.<sup id="cite_ref-Myerson_1-1" class="reference"><a href="#cite_note-Myerson-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> Hurwicz introduced and formalized the concept of <a href="/wiki/Incentive_compatibility" title="Incentive compatibility">incentive compatibility</a>. </p><p>In 2012, <a href="/wiki/Alvin_E._Roth" title="Alvin E. Roth">Alvin E. Roth</a> and <a href="/wiki/Lloyd_Shapley" title="Lloyd Shapley">Lloyd S. Shapley</a> were awarded the Nobel Prize in Economics "for the theory of stable allocations and the practice of market design". In 2014, the Nobel went to game theorist <a href="/wiki/Jean_Tirole" title="Jean Tirole">Jean Tirole</a>. </p> <div class="mw-heading mw-heading2"><h2 id="Different_types_of_games">Different types of games</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Game_theory&action=edit&section=5" title="Edit section: Different types of games"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">See also: <a href="/wiki/List_of_games_in_game_theory" title="List of games in game theory">List of games in game theory</a></div> <div class="mw-heading mw-heading3"><h3 id="Cooperative_/_non-cooperative"><span id="Cooperative_.2F_non-cooperative"></span>Cooperative / non-cooperative</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Game_theory&action=edit&section=6" title="Edit section: Cooperative / non-cooperative"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main articles: <a href="/wiki/Cooperative_game_theory" title="Cooperative game theory">Cooperative game theory</a> and <a href="/wiki/Non-cooperative_game" class="mw-redirect" title="Non-cooperative game">Non-cooperative game</a></div> <p>A game is <i>cooperative</i> if the players are able to form binding commitments externally enforced (e.g. through <a href="/wiki/Contract_law" class="mw-redirect" title="Contract law">contract law</a>). A game is <i>non-cooperative</i> if players cannot form alliances or if all agreements need to be <a href="/wiki/Self-enforcing_agreement" title="Self-enforcing agreement">self-enforcing</a> (e.g. through <a href="/wiki/Credible_threat" class="mw-redirect" title="Credible threat">credible threats</a>).<sup id="cite_ref-17" class="reference"><a href="#cite_note-17"><span class="cite-bracket">[</span>16<span class="cite-bracket">]</span></a></sup> </p><p>Cooperative games are often analyzed through the framework of <i>cooperative game theory</i>, which focuses on predicting which coalitions will form, the joint actions that groups take, and the resulting collective payoffs. It is different from <i>non-cooperative game theory</i> which focuses on predicting individual players' actions and payoffs by analyzing <a href="/wiki/Nash_equilibria" class="mw-redirect" title="Nash equilibria">Nash equilibria</a>.<sup id="cite_ref-18" class="reference"><a href="#cite_note-18"><span class="cite-bracket">[</span>17<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-19" class="reference"><a href="#cite_note-19"><span class="cite-bracket">[</span>18<span class="cite-bracket">]</span></a></sup> </p><p>Cooperative game theory provides a high-level approach as it describes only the structure and payoffs of coalitions, whereas non-cooperative game theory also looks at how strategic interaction will affect the distribution of payoffs. As non-cooperative game theory is more general, cooperative games can be analyzed through the approach of non-cooperative game theory (the converse does not hold) provided that sufficient assumptions are made to encompass all the possible strategies available to players due to the possibility of external enforcement of cooperation. </p> <div class="mw-heading mw-heading3"><h3 id="Symmetric_/_asymmetric"><span id="Symmetric_.2F_asymmetric"></span>Symmetric / asymmetric</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Game_theory&action=edit&section=7" title="Edit section: Symmetric / asymmetric"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <table id="Payoff_matrix" style="background:white; float: right; clear:right; text-align:center;" align="right" cellspacing="0" cellpadding="8" width="225"> <tbody><tr> <td style="width:33%;"> </td> <td style="width:33%; border-bottom: solid black 1px;">E </td> <td style="width:33%; border-bottom: solid black 1px;">F </td></tr> <tr> <td style="border-right: solid black 1px; text-align: right;">E </td> <td style="border-right: solid black 1px; border-bottom: solid black 1px; background:white; font-size:120%; white-space:nowrap;">1, 2 </td> <td style="border-right: solid black 1px; border-bottom: solid black 1px; background:white; font-size:120%; white-space:nowrap;">0, 0 </td></tr> <tr> <td style="border-right: solid black 1px; text-align: right;">F </td> <td style="border-right: solid black 1px; border-bottom: solid black 1px; background:white; font-size:120%; white-space:nowrap;">0, 0 </td> <td style="border-right: solid black 1px; border-bottom: solid black 1px; background:white; font-size:120%; white-space:nowrap;">1, 2 </td></tr> <tr> <td style="font-size: 90%;" colspan="3"><i>An asymmetric game</i> </td></tr></tbody></table> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Symmetric_game" title="Symmetric game">Symmetric game</a></div> <p>A symmetric game is a game where each player earns the same payoff when making the same choice. In other words, the identity of the player does not change the resulting game facing the other player.<sup id="cite_ref-20" class="reference"><a href="#cite_note-20"><span class="cite-bracket">[</span>19<span class="cite-bracket">]</span></a></sup> Many of the commonly studied 2×2 games are symmetric. The standard representations of <a href="/wiki/Game_of_chicken" class="mw-redirect" title="Game of chicken">chicken</a>, the prisoner's dilemma, and the <a href="/wiki/Stag_hunt" title="Stag hunt">stag hunt</a> are all symmetric games. </p><p>The most commonly studied asymmetric games are games where there are not identical strategy sets for both players. For instance, the <a href="/wiki/Ultimatum_game" title="Ultimatum game">ultimatum game</a> and similarly the <a href="/wiki/Dictator_game" title="Dictator game">dictator game</a> have different strategies for each player. It is possible, however, for a game to have identical strategies for both players, yet be asymmetric. For example, the game pictured in this section's graphic is asymmetric despite having identical strategy sets for both players. </p> <div class="mw-heading mw-heading3"><h3 id="Zero-sum_/_non-zero-sum"><span id="Zero-sum_.2F_non-zero-sum"></span>Zero-sum / non-zero-sum</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Game_theory&action=edit&section=8" title="Edit section: Zero-sum / non-zero-sum"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <table id="Payoff_matrix" style="background:white; float: right; clear:right; text-align:center;" align="right" cellspacing="0" cellpadding="8" width="225"> <tbody><tr> <td style="width:33%;"> </td> <td style="width:33%; border-bottom: solid black 1px;">A </td> <td style="width:33%; border-bottom: solid black 1px;">B </td></tr> <tr> <td style="border-right: solid black 1px; text-align: right;">A </td> <td style="border-right: solid black 1px; border-bottom: solid black 1px; background:white; font-size:120%; white-space:nowrap;">–1, 1 </td> <td style="border-right: solid black 1px; border-bottom: solid black 1px; background:white; font-size:120%; white-space:nowrap;">3, −3 </td></tr> <tr> <td style="border-right: solid black 1px; text-align: right;">B </td> <td style="border-right: solid black 1px; border-bottom: solid black 1px; background:white; font-size:120%; white-space:nowrap;">0, 0 </td> <td style="border-right: solid black 1px; border-bottom: solid black 1px; background:white; font-size:120%; white-space:nowrap;">–2, 2 </td></tr> <tr> <td style="font-size: 90%;" colspan="3"><i>A zero-sum game</i> </td></tr></tbody></table> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Zero-sum_game" title="Zero-sum game">Zero-sum game</a></div> <p>Zero-sum games (more generally, constant-sum games) are games in which choices by players can neither increase nor decrease the available resources. In zero-sum games, the total benefit goes to all players in a game, for every combination of strategies, and always adds to zero (more informally, a player benefits only at the equal expense of others).<sup id="cite_ref-21" class="reference"><a href="#cite_note-21"><span class="cite-bracket">[</span>20<span class="cite-bracket">]</span></a></sup> <a href="/wiki/Poker" title="Poker">Poker</a> exemplifies a zero-sum game (ignoring the possibility of the house's cut), because one wins exactly the amount one's opponents lose. Other zero-sum games include <a href="/wiki/Matching_pennies" title="Matching pennies">matching pennies</a> and most classical board games including <a href="/wiki/Go_(board_game)" class="mw-redirect" title="Go (board game)">Go</a> and <a href="/wiki/Chess" title="Chess">chess</a>. </p><p>Many games studied by game theorists (including the famed prisoner's dilemma) are non-zero-sum games, because the <a href="/wiki/Outcome_(game_theory)" title="Outcome (game theory)">outcome</a> has net results greater or less than zero. Informally, in non-zero-sum games, a gain by one player does not necessarily correspond with a loss by another. </p><p>Furthermore, <i>constant-sum games</i> correspond to activities like theft and gambling, but not to the fundamental economic situation in which there are potential <a href="/wiki/Gains_from_trade" title="Gains from trade">gains from trade</a>. It is possible to transform any constant-sum game into a (possibly asymmetric) zero-sum game by adding a dummy player (often called "the board") whose losses compensate the players' net winnings. </p> <div class="mw-heading mw-heading3"><h3 id="Simultaneous_/_sequential"><span id="Simultaneous_.2F_sequential"></span>Simultaneous / sequential</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Game_theory&action=edit&section=9" title="Edit section: Simultaneous / sequential"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main articles: <a href="/wiki/Simultaneous_game" title="Simultaneous game">Simultaneous game</a> and <a href="/wiki/Sequential_game" title="Sequential game">Sequential game</a></div> <p><a href="/wiki/Simultaneous_game" title="Simultaneous game">Simultaneous games</a> are games where both players move simultaneously, or instead the later players are unaware of the earlier players' actions (making them <i>effectively</i> simultaneous). <a href="/wiki/Sequential_game" title="Sequential game">Sequential games</a> (or dynamic games) are games where players do not make decisions simultaneously, and player's earlier actions affect the outcome and decisions of other players.<sup id="cite_ref-22" class="reference"><a href="#cite_note-22"><span class="cite-bracket">[</span>21<span class="cite-bracket">]</span></a></sup> This need not be <a href="/wiki/Perfect_information" title="Perfect information">perfect information</a> about every action of earlier players; it might be very little knowledge. For instance, a player may know that an earlier player did not perform one particular action, while they do not know which of the other available actions the first player actually performed. </p><p>The difference between simultaneous and sequential games is captured in the different representations discussed above. Often, <a href="/wiki/Normal_form_game" class="mw-redirect" title="Normal form game">normal form</a> is used to represent simultaneous games, while <a href="/wiki/Extensive_form_game" class="mw-redirect" title="Extensive form game">extensive form</a> is used to represent sequential ones. The transformation of extensive to normal form is one way, meaning that multiple extensive form games correspond to the same normal form. Consequently, notions of equilibrium for simultaneous games are insufficient for reasoning about sequential games; see <a href="/wiki/Subgame_perfection" class="mw-redirect" title="Subgame perfection">subgame perfection</a>. </p><p>In short, the differences between sequential and simultaneous games are as follows: </p> <table class="wikitable"> <tbody><tr> <th></th> <th>Sequential</th> <th>Simultaneous </th></tr> <tr> <td>Normally denoted by</td> <td><a href="/wiki/Decision_tree" title="Decision tree">Decision trees</a></td> <td><a href="/wiki/Payoff_matrix" class="mw-redirect" title="Payoff matrix">Payoff matrices</a> </td></tr> <tr> <td><div style="display: inline-block; line-height: 1.2em; padding: .1em 0; line-height:1.3em;padding-right:0.65em">Prior knowledge<br />of opponent's move?</div></td> <td>Yes</td> <td>No </td></tr> <tr> <td>Time axis?</td> <td>Yes</td> <td>No </td></tr> <tr> <td>Also known as</td> <td><div style="display: inline-block; line-height: 1.2em; padding: .1em 0; line-height:1.3em"><a href="/wiki/Extensive-form_game" title="Extensive-form game">Extensive-form game</a><br />Extensive game</div></td> <td><div style="display: inline-block; line-height: 1.2em; padding: .1em 0; line-height:1.3em"><a href="/wiki/Strategy_game" title="Strategy game">Strategy game</a><br />Strategic game</div> </td></tr></tbody></table> <div class="mw-heading mw-heading3"><h3 id="Perfect_information_and_imperfect_information">Perfect information and imperfect information</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Game_theory&action=edit&section=10" title="Edit section: Perfect information and imperfect information"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Perfect_information" title="Perfect information">Perfect information</a></div> <figure class="mw-default-size mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:PD_with_outside_option.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/2/23/PD_with_outside_option.svg/280px-PD_with_outside_option.svg.png" decoding="async" width="280" height="127" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/2/23/PD_with_outside_option.svg/420px-PD_with_outside_option.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/2/23/PD_with_outside_option.svg/560px-PD_with_outside_option.svg.png 2x" data-file-width="214" data-file-height="97" /></a><figcaption>A game of imperfect information. The dotted line represents ignorance on the part of player 2, formally called an <a href="/wiki/Information_set_(game_theory)" title="Information set (game theory)">information set</a>.</figcaption></figure> <p>An important subset of sequential games consists of games of perfect information. A game with perfect information means that all players, at every move in the game, know the previous history of the game and the moves previously made by all other players. An imperfect information game is played when the players do not know all moves already made by the opponent such as a simultaneous move game.<sup id="cite_ref-:2_23-0" class="reference"><a href="#cite_note-:2-23"><span class="cite-bracket">[</span>22<span class="cite-bracket">]</span></a></sup> Examples of perfect-information games include <a href="/wiki/Tic-tac-toe" title="Tic-tac-toe">tic-tac-toe</a>, <a href="/wiki/Draughts" class="mw-redirect" title="Draughts">checkers</a>, <a href="/wiki/Chess" title="Chess">chess</a>, and <a href="/wiki/Go_(board_game)" class="mw-redirect" title="Go (board game)">Go</a>.<sup id="cite_ref-24" class="reference"><a href="#cite_note-24"><span class="cite-bracket">[</span>23<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-25" class="reference"><a href="#cite_note-25"><span class="cite-bracket">[</span>24<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-26" class="reference"><a href="#cite_note-26"><span class="cite-bracket">[</span>25<span class="cite-bracket">]</span></a></sup> </p><p>Many card games are games of imperfect information, such as <a href="/wiki/Poker" title="Poker">poker</a> and <a href="/wiki/Contract_bridge" title="Contract bridge">bridge</a>.<sup id="cite_ref-27" class="reference"><a href="#cite_note-27"><span class="cite-bracket">[</span>26<span class="cite-bracket">]</span></a></sup> Perfect information is often confused with <a href="/wiki/Complete_information" title="Complete information">complete information</a>, which is a similar concept pertaining to the common knowledge of each player's sequence, strategies, and payoffs throughout gameplay.<sup id="cite_ref-28" class="reference"><a href="#cite_note-28"><span class="cite-bracket">[</span>27<span class="cite-bracket">]</span></a></sup> Complete information requires that every player know the strategies and payoffs available to the other players but not necessarily the actions taken, whereas perfect information is knowledge of all aspects of the game and players.<sup id="cite_ref-29" class="reference"><a href="#cite_note-29"><span class="cite-bracket">[</span>28<span class="cite-bracket">]</span></a></sup> Games of <a href="/wiki/Information_asymmetry" title="Information asymmetry">incomplete information</a> can be reduced, however, to games of imperfect information by introducing "<a href="/wiki/Move_by_nature" title="Move by nature">moves by nature</a>".<sup id="cite_ref-FOOTNOTEShohamLeyton-Brown200860_30-0" class="reference"><a href="#cite_note-FOOTNOTEShohamLeyton-Brown200860-30"><span class="cite-bracket">[</span>29<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Bayesian_game">Bayesian game</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Game_theory&action=edit&section=11" title="Edit section: Bayesian game"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Bayesian_game" title="Bayesian game">Bayesian game</a></div> <p>One of the assumptions of the Nash equilibrium is that every player has correct beliefs about the actions of the other players. However, there are many situations in game theory where participants do not fully understand the characteristics of their opponents. Negotiators may be unaware of their opponent's valuation of the object of negotiation, companies may be unaware of their opponent's cost functions, combatants may be unaware of their opponent's strengths, and jurors may be unaware of their colleague's interpretation of the evidence at trial. In some cases, participants may know the character of their opponent well, but may not know how well their opponent knows his or her own character.<sup id="cite_ref-31" class="reference"><a href="#cite_note-31"><span class="cite-bracket">[</span>30<span class="cite-bracket">]</span></a></sup> </p><p><a href="/wiki/Bayesian_game" title="Bayesian game">Bayesian game</a> means a strategic game with incomplete information. For a strategic game, decision makers are players, and every player has a group of actions. A core part of the imperfect information specification is the set of states. Every state completely describes a collection of characteristics relevant to the player such as their preferences and details about them. There must be a state for every set of features that some player believes may exist.<sup id="cite_ref-32" class="reference"><a href="#cite_note-32"><span class="cite-bracket">[</span>31<span class="cite-bracket">]</span></a></sup> </p> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:An_example_of_diagram.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/8/8c/An_example_of_diagram.jpg/220px-An_example_of_diagram.jpg" decoding="async" width="220" height="117" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/8/8c/An_example_of_diagram.jpg/330px-An_example_of_diagram.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/8/8c/An_example_of_diagram.jpg/440px-An_example_of_diagram.jpg 2x" data-file-width="1360" data-file-height="726" /></a><figcaption>Example of a Bayesian game</figcaption></figure> <p>For example, where Player 1 is unsure whether Player 2 would rather date her or get away from her, while Player 2 understands Player 1's preferences as before. To be specific, supposing that Player 1 believes that Player 2 wants to date her under a probability of 1/2 and get away from her under a probability of 1/2 (this evaluation comes from Player 1's experience probably: she faces players who want to date her half of the time in such a case and players who want to avoid her half of the time). Due to the probability involved, the analysis of this situation requires to understand the player's preference for the draw, even though people are only interested in pure strategic equilibrium. </p> <div class="mw-heading mw-heading3"><h3 id="Combinatorial_games">Combinatorial games</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Game_theory&action=edit&section=12" title="Edit section: Combinatorial games"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Games in which the difficulty of finding an optimal strategy stems from the multiplicity of possible moves are called combinatorial games. Examples include chess and <a href="/wiki/Go_(game)" title="Go (game)">Go</a>. Games that involve <a href="/wiki/Perfect_information" title="Perfect information">imperfect information</a> may also have a strong combinatorial character, for instance <a href="/wiki/Backgammon" title="Backgammon">backgammon</a>. There is no unified theory addressing combinatorial elements in games. There are, however, mathematical tools that can solve some particular problems and answer some general questions.<sup id="cite_ref-Bewersdorff2005_33-0" class="reference"><a href="#cite_note-Bewersdorff2005-33"><span class="cite-bracket">[</span>32<span class="cite-bracket">]</span></a></sup> </p><p>Games of perfect information have been studied in <a href="/wiki/Combinatorial_game_theory" title="Combinatorial game theory">combinatorial game theory</a>, which has developed novel representations, e.g. <a href="/wiki/Surreal_numbers" class="mw-redirect" title="Surreal numbers">surreal numbers</a>, as well as <a href="/wiki/Combinatorics" title="Combinatorics">combinatorial</a> and <a href="/wiki/Abstract_algebra" title="Abstract algebra">algebraic</a> (and <a href="/wiki/Strategy_stealing_argument" class="mw-redirect" title="Strategy stealing argument">sometimes non-constructive</a>) proof methods to <a href="/wiki/Solved_game" title="Solved game">solve games</a> of certain types, including "loopy" games that may result in infinitely long sequences of moves. These methods address games with higher combinatorial complexity than those usually considered in traditional (or "economic") game theory.<sup id="cite_ref-34" class="reference"><a href="#cite_note-34"><span class="cite-bracket">[</span>33<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-35" class="reference"><a href="#cite_note-35"><span class="cite-bracket">[</span>34<span class="cite-bracket">]</span></a></sup> A typical game that has been solved this way is <a href="/wiki/Hex_(board_game)" title="Hex (board game)">Hex</a>. A related field of study, drawing from <a href="/wiki/Computational_complexity_theory" title="Computational complexity theory">computational complexity theory</a>, is <a href="/wiki/Game_complexity" title="Game complexity">game complexity</a>, which is concerned with estimating the computational difficulty of finding optimal strategies.<sup id="cite_ref-36" class="reference"><a href="#cite_note-36"><span class="cite-bracket">[</span>35<span class="cite-bracket">]</span></a></sup> </p><p>Research in <a href="/wiki/Artificial_intelligence" title="Artificial intelligence">artificial intelligence</a> has addressed both perfect and imperfect information games that have very complex combinatorial structures (like chess, go, or backgammon) for which no provable optimal strategies have been found. The practical solutions involve computational heuristics, like <a href="/wiki/Alpha%E2%80%93beta_pruning" title="Alpha–beta pruning">alpha–beta pruning</a> or use of <a href="/wiki/Artificial_neural_network" class="mw-redirect" title="Artificial neural network">artificial neural networks</a> trained by <a href="/wiki/Reinforcement_learning" title="Reinforcement learning">reinforcement learning</a>, which make games more tractable in computing practice.<sup id="cite_ref-Bewersdorff2005_33-1" class="reference"><a href="#cite_note-Bewersdorff2005-33"><span class="cite-bracket">[</span>32<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-Jones2008_37-0" class="reference"><a href="#cite_note-Jones2008-37"><span class="cite-bracket">[</span>36<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Discrete_and_continuous_games">Discrete and continuous games</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Game_theory&action=edit&section=13" title="Edit section: Discrete and continuous games"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Much of game theory is concerned with finite, discrete games that have a finite number of players, moves, events, outcomes, etc. Many concepts can be extended, however. <a href="/wiki/Continuous_game" title="Continuous game">Continuous games</a> allow players to choose a strategy from a continuous strategy set. For instance, <a href="/wiki/Cournot_competition" title="Cournot competition">Cournot competition</a> is typically modeled with players' strategies being any non-negative quantities, including fractional quantities. </p> <div class="mw-heading mw-heading3"><h3 id="Differential_games">Differential games</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Game_theory&action=edit&section=14" title="Edit section: Differential games"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Differential_game" title="Differential game">Differential game</a></div> <p>Differential games such as the continuous <a href="/wiki/Pursuit-evasion" class="mw-redirect" title="Pursuit-evasion">pursuit and evasion game</a> are continuous games where the evolution of the players' state variables is governed by <a href="/wiki/Differential_equation" title="Differential equation">differential equations</a>. The problem of finding an optimal strategy in a differential game is closely related to the <a href="/wiki/Optimal_control" title="Optimal control">optimal control</a> theory. In particular, there are two types of strategies: the open-loop strategies are found using the <a href="/wiki/Pontryagin%27s_Minimum_Principle" class="mw-redirect" title="Pontryagin's Minimum Principle">Pontryagin maximum principle</a> while the closed-loop strategies are found using <a href="/wiki/Hamilton%E2%80%93Jacobi%E2%80%93Bellman_equation" title="Hamilton–Jacobi–Bellman equation">Bellman's Dynamic Programming</a> method. </p><p>A particular case of differential games are the games with a random <a href="/wiki/Time_horizon" title="Time horizon">time horizon</a>.<sup id="cite_ref-PM66_38-0" class="reference"><a href="#cite_note-PM66-38"><span class="cite-bracket">[</span>37<span class="cite-bracket">]</span></a></sup> In such games, the terminal time is a random variable with a given <a href="/wiki/Probability_distribution" title="Probability distribution">probability distribution</a> function. Therefore, the players maximize the <a href="/wiki/Mathematical_expectation" class="mw-redirect" title="Mathematical expectation">mathematical expectation</a> of the cost function. It was shown that the modified optimization problem can be reformulated as a discounted differential game over an infinite time interval. </p> <div class="mw-heading mw-heading3"><h3 id="Evolutionary_game_theory">Evolutionary game theory</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Game_theory&action=edit&section=15" title="Edit section: Evolutionary game theory"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Evolutionary_game_theory" title="Evolutionary game theory">Evolutionary game theory</a></div> <p>Evolutionary game theory studies players who adjust their strategies over time according to rules that are not necessarily rational or farsighted.<sup id="cite_ref-Newton2018renaissance_39-0" class="reference"><a href="#cite_note-Newton2018renaissance-39"><span class="cite-bracket">[</span>38<span class="cite-bracket">]</span></a></sup> In general, the evolution of strategies over time according to such rules is modeled as a <a href="/wiki/Markov_chain" title="Markov chain">Markov chain</a> with a state variable such as the current strategy profile or how the game has been played in the recent past. Such rules may feature imitation, optimization, or survival of the fittest. </p><p>In biology, such models can represent <a href="/wiki/Evolution" title="Evolution">evolution</a>, in which offspring adopt their parents' strategies and parents who play more successful strategies (i.e. corresponding to higher payoffs) have a greater number of offspring. In the social sciences, such models typically represent strategic adjustment by players who play a game many times within their lifetime and, consciously or unconsciously, occasionally adjust their strategies.<sup id="cite_ref-FOOTNOTEWebb2007_40-0" class="reference"><a href="#cite_note-FOOTNOTEWebb2007-40"><span class="cite-bracket">[</span>39<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Stochastic_outcomes_(and_relation_to_other_fields)"><span id="Stochastic_outcomes_.28and_relation_to_other_fields.29"></span>Stochastic outcomes (and relation to other fields)</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Game_theory&action=edit&section=16" title="Edit section: Stochastic outcomes (and relation to other fields)"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Individual decision problems with stochastic outcomes are sometimes considered "one-player games". They may be modeled using similar tools within the related disciplines of <a href="/wiki/Decision_theory" title="Decision theory">decision theory</a>, <a href="/wiki/Operations_research" title="Operations research">operations research</a>, and areas of <a href="/wiki/Artificial_intelligence" title="Artificial intelligence">artificial intelligence</a>, particularly <a href="/wiki/AI_planning" class="mw-redirect" title="AI planning">AI planning</a> (with uncertainty) and <a href="/wiki/Multi-agent_system" title="Multi-agent system">multi-agent system</a>. Although these fields may have different motivators, the mathematics involved are substantially the same, e.g. using <a href="/wiki/Markov_decision_process" title="Markov decision process">Markov decision processes</a> (MDP).<sup id="cite_ref-41" class="reference"><a href="#cite_note-41"><span class="cite-bracket">[</span>40<span class="cite-bracket">]</span></a></sup> </p><p>Stochastic outcomes can also be modeled in terms of game theory by adding a randomly acting player who makes "chance moves" ("<a href="/wiki/Move_by_nature" title="Move by nature">moves by nature</a>").<sup id="cite_ref-FOOTNOTEOsborneRubinstein1994_42-0" class="reference"><a href="#cite_note-FOOTNOTEOsborneRubinstein1994-42"><span class="cite-bracket">[</span>41<span class="cite-bracket">]</span></a></sup> This player is not typically considered a third player in what is otherwise a two-player game, but merely serves to provide a roll of the dice where required by the game. </p><p>For some problems, different approaches to modeling stochastic outcomes may lead to different solutions. For example, the difference in approach between MDPs and the <a href="/wiki/Minimax" title="Minimax">minimax solution</a> is that the latter considers the worst-case over a set of adversarial moves, rather than reasoning in expectation about these moves given a fixed probability distribution. The minimax approach may be advantageous where stochastic models of uncertainty are not available, but may also be overestimating extremely unlikely (but costly) events, dramatically swaying the strategy in such scenarios if it is assumed that an adversary can force such an event to happen.<sup id="cite_ref-McMahan_43-0" class="reference"><a href="#cite_note-McMahan-43"><span class="cite-bracket">[</span>42<span class="cite-bracket">]</span></a></sup> (See <a href="/wiki/Black_swan_theory" title="Black swan theory">Black swan theory</a> for more discussion on this kind of modeling issue, particularly as it relates to predicting and limiting losses in investment banking.) </p><p>General models that include all elements of stochastic outcomes, adversaries, and partial or noisy observability (of moves by other players) have also been studied. The "<a href="/wiki/Gold_standard" title="Gold standard">gold standard</a>" is considered to be partially observable <a href="/wiki/Stochastic_game" title="Stochastic game">stochastic game</a> (POSG), but few realistic problems are computationally feasible in POSG representation.<sup id="cite_ref-McMahan_43-1" class="reference"><a href="#cite_note-McMahan-43"><span class="cite-bracket">[</span>42<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Metagames">Metagames</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Game_theory&action=edit&section=17" title="Edit section: Metagames"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>These are games the play of which is the development of the rules for another game, the target or subject game. <a href="/wiki/Metagame" title="Metagame">Metagames</a> seek to maximize the utility value of the rule set developed. The theory of metagames is related to <a href="/wiki/Mechanism_design" title="Mechanism design">mechanism design</a> theory. </p><p>The term <a href="/wiki/Metagame_analysis" title="Metagame analysis">metagame analysis</a> is also used to refer to a practical approach developed by Nigel Howard,<sup id="cite_ref-FOOTNOTEHoward1971_44-0" class="reference"><a href="#cite_note-FOOTNOTEHoward1971-44"><span class="cite-bracket">[</span>43<span class="cite-bracket">]</span></a></sup> whereby a situation is framed as a strategic game in which stakeholders try to realize their objectives by means of the options available to them. Subsequent developments have led to the formulation of <a href="/wiki/Confrontation_analysis" title="Confrontation analysis">confrontation analysis</a>. </p> <div class="mw-heading mw-heading3"><h3 id="Mean_field_game_theory">Mean field game theory</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Game_theory&action=edit&section=18" title="Edit section: Mean field game theory"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Mean_field_game_theory" class="mw-redirect" title="Mean field game theory">Mean field game theory</a></div> <p>Mean field game theory is the study of strategic decision making in very large populations of small interacting agents. This class of problems was considered in the economics literature by <a href="/wiki/Boyan_Jovanovic" title="Boyan Jovanovic">Boyan Jovanovic</a> and <a href="/wiki/Robert_W._Rosenthal" title="Robert W. Rosenthal">Robert W. Rosenthal</a>, in the engineering literature by <a href="/wiki/Peter_E._Caines" title="Peter E. Caines">Peter E. Caines</a>, and by mathematicians <a href="/wiki/Pierre-Louis_Lions" title="Pierre-Louis Lions">Pierre-Louis Lions</a> and Jean-Michel Lasry. </p> <div class="mw-heading mw-heading2"><h2 id="Representation_of_games">Representation of games</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Game_theory&action=edit&section=19" title="Edit section: Representation of games"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The games studied in game theory are well-defined mathematical objects. To be fully defined, a game must specify the following elements: the <i>players</i> of the game, the <i>information</i> and <i>actions</i> available to each player at each decision point, and the <a href="/wiki/Utility" title="Utility"><i>payoffs</i></a> for each outcome. (Eric Rasmusen refers to these four "essential elements" by the acronym "PAPI".)<sup id="cite_ref-r7a_45-0" class="reference"><a href="#cite_note-r7a-45"><span class="cite-bracket">[</span>44<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-r7b_46-0" class="reference"><a href="#cite_note-r7b-46"><span class="cite-bracket">[</span>45<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-r7c_47-0" class="reference"><a href="#cite_note-r7c-47"><span class="cite-bracket">[</span>46<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-r7d_48-0" class="reference"><a href="#cite_note-r7d-48"><span class="cite-bracket">[</span>47<span class="cite-bracket">]</span></a></sup> A game theorist typically uses these elements, along with a <a href="/wiki/Solution_concept" title="Solution concept">solution concept</a> of their choosing, to deduce a set of equilibrium <a href="/wiki/Strategy_(game_theory)" title="Strategy (game theory)">strategies</a> for each player such that, when these strategies are employed, no player can profit by unilaterally deviating from their strategy. These equilibrium strategies determine an <a href="/wiki/Economic_equilibrium" title="Economic equilibrium">equilibrium</a> to the game—a stable state in which either one outcome occurs or a set of outcomes occur with known probability. </p><p>Most cooperative games are presented in the characteristic function form, while the extensive and the normal forms are used to define noncooperative games. </p> <div class="mw-heading mw-heading3"><h3 id="Extensive_form">Extensive form</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Game_theory&action=edit&section=20" title="Edit section: Extensive form"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Extensive_form_game" class="mw-redirect" title="Extensive form game">Extensive form game</a></div> <figure class="mw-default-size mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:Ultimatum_Game_Extensive_Form.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/b/be/Ultimatum_Game_Extensive_Form.svg/220px-Ultimatum_Game_Extensive_Form.svg.png" decoding="async" width="220" height="110" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/b/be/Ultimatum_Game_Extensive_Form.svg/330px-Ultimatum_Game_Extensive_Form.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/b/be/Ultimatum_Game_Extensive_Form.svg/440px-Ultimatum_Game_Extensive_Form.svg.png 2x" data-file-width="148" data-file-height="74" /></a><figcaption>An extensive form game</figcaption></figure> <p>The extensive form can be used to formalize games with a time sequencing of moves. Extensive form games can be visualized using game <a href="/wiki/Tree_(graph_theory)" title="Tree (graph theory)">trees</a> (as pictured here). Here each <a href="/wiki/Graph_(discrete_mathematics)" title="Graph (discrete mathematics)">vertex</a> (or node) represents a point of choice for a player. The player is specified by a number listed by the vertex. The lines out of the vertex represent a possible action for that player. The payoffs are specified at the bottom of the tree. The extensive form can be viewed as a multi-player generalization of a <a href="/wiki/Decision_tree" title="Decision tree">decision tree</a>.<sup id="cite_ref-49" class="reference"><a href="#cite_note-49"><span class="cite-bracket">[</span>48<span class="cite-bracket">]</span></a></sup> To solve any extensive form game, <a href="/wiki/Backward_induction" title="Backward induction">backward induction</a> must be used. It involves working backward up the game tree to determine what a rational player would do at the last vertex of the tree, what the player with the previous move would do given that the player with the last move is rational, and so on until the first vertex of the tree is reached.<sup id="cite_ref-50" class="reference"><a href="#cite_note-50"><span class="cite-bracket">[</span>49<span class="cite-bracket">]</span></a></sup> </p><p>The game pictured consists of two players. The way this particular game is structured (i.e., with sequential decision making and perfect information), <i>Player 1</i> "moves" first by choosing either <var style="padding-right: 1px;">F</var> or <var style="padding-right: 1px;">U</var> (fair or unfair). Next in the sequence, <i>Player 2</i>, who has now observed <i>Player 1</i><span class="nowrap" style="padding-left:0.1em;">'</span>s move, can choose to play either <var style="padding-right: 1px;">A</var> or <var style="padding-right: 1px;">R</var> (accept or reject). Once <i>Player 2</i> has made their choice, the game is considered finished and each player gets their respective payoff, represented in the image as two numbers, where the first number represents Player 1's payoff, and the second number represents Player 2's payoff. Suppose that <i>Player 1</i> chooses <var style="padding-right: 1px;">U</var> and then <i>Player 2</i> chooses <var style="padding-right: 1px;">A</var>: <i>Player 1</i> then gets a payoff of "eight" (which in real-world terms can be interpreted in many ways, the simplest of which is in terms of money but could mean things such as eight days of vacation or eight countries conquered or even eight more opportunities to play the same game against other players) and <i>Player 2</i> gets a payoff of "two". </p><p>The extensive form can also capture simultaneous-move games and games with imperfect information. To represent it, either a dotted line connects different vertices to represent them as being part of the same information set (i.e. the players do not know at which point they are), or a closed line is drawn around them. (See example in the <a href="#Perfect_information_and_imperfect_information">imperfect information section</a>.) </p> <div class="mw-heading mw-heading3"><h3 id="Normal_form">Normal form</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Game_theory&action=edit&section=21" title="Edit section: Normal form"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <table id="Payoff_matrix" style="background:white; float: right; clear:right; text-align:center;" align="right" cellspacing="0" cellpadding="8" width="330"> <tbody><tr> <td style="width:33%;"> </td> <td style="width:33%; border-bottom: solid black 1px;"><style data-mw-deduplicate="TemplateStyles:r1239334494">@media screen{html.skin-theme-clientpref-night .mw-parser-output div:not(.notheme)>.tmp-color,html.skin-theme-clientpref-night .mw-parser-output p>.tmp-color,html.skin-theme-clientpref-night .mw-parser-output table:not(.notheme) .tmp-color{color:inherit!important}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output div:not(.notheme)>.tmp-color,html.skin-theme-clientpref-os .mw-parser-output p>.tmp-color,html.skin-theme-clientpref-os .mw-parser-output table:not(.notheme) .tmp-color{color:inherit!important}}</style><span class="tmp-color" style="color:#900">Player 2<br />chooses <i>Left</i></span> </td> <td style="width:33%; border-bottom: solid black 1px;"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1239334494"><span class="tmp-color" style="color:#900">Player 2<br />chooses <i>Right</i></span> </td></tr> <tr> <td style="border-right: solid black 1px; text-align: right;"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1239334494"><span class="tmp-color" style="color:#009">Player 1<br />chooses <i>Up</i></span> </td> <td style="border-right: solid black 1px; border-bottom: solid black 1px; background:white; font-size:120%; white-space:nowrap;"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1239334494"><span class="tmp-color" style="color:#009"><b>4</b></span>, <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1239334494"><span class="tmp-color" style="color:#900"><b>3</b></span> </td> <td style="border-right: solid black 1px; border-bottom: solid black 1px; background:white; font-size:120%; white-space:nowrap;"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1239334494"><span class="tmp-color" style="color:#009"><b>–1</b></span>, <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1239334494"><span class="tmp-color" style="color:#900"><b>–1</b></span> </td></tr> <tr> <td style="border-right: solid black 1px; text-align: right;"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1239334494"><span class="tmp-color" style="color:#009">Player 1<br />chooses <i>Down</i></span> </td> <td style="border-right: solid black 1px; border-bottom: solid black 1px; background:white; font-size:120%; white-space:nowrap;"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1239334494"><span class="tmp-color" style="color:#009"><b>0</b></span>, <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1239334494"><span class="tmp-color" style="color:#900"><b>0</b></span> </td> <td style="border-right: solid black 1px; border-bottom: solid black 1px; background:white; font-size:120%; white-space:nowrap;"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1239334494"><span class="tmp-color" style="color:#009"><b>3</b></span>, <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1239334494"><span class="tmp-color" style="color:#900"><b>4</b></span> </td></tr> <tr> <td style="font-size: 90%;" colspan="3"><i>Normal form or payoff matrix of a 2-player, 2-strategy game</i> </td></tr></tbody></table> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Normal-form_game" title="Normal-form game">Normal-form game</a></div> <p>The normal (or strategic form) game is usually represented by a <a href="/wiki/Matrix_(mathematics)" title="Matrix (mathematics)">matrix</a> which shows the players, strategies, and payoffs (see the example to the right). More generally it can be represented by any function that associates a payoff for each player with every possible combination of actions. In the accompanying example there are two players; one chooses the row and the other chooses the column. Each player has two strategies, which are specified by the number of rows and the number of columns. The payoffs are provided in the interior. The first number is the payoff received by the row player (Player 1 in our example); the second is the payoff for the column player (Player 2 in our example). Suppose that Player 1 plays <i>Up</i> and that Player 2 plays <i>Left</i>. Then Player 1 gets a payoff of 4, and Player 2 gets 3. </p><p>When a game is presented in normal form, it is presumed that each player acts simultaneously or, at least, without knowing the actions of the other. If players have some information about the choices of other players, the game is usually presented in extensive form. </p><p>Every extensive-form game has an equivalent normal-form game, however, the transformation to normal form may result in an exponential blowup in the size of the representation, making it computationally impractical.<sup id="cite_ref-FOOTNOTEShohamLeyton-Brown200835_51-0" class="reference"><a href="#cite_note-FOOTNOTEShohamLeyton-Brown200835-51"><span class="cite-bracket">[</span>50<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Characteristic_function_form">Characteristic function form</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Game_theory&action=edit&section=22" title="Edit section: Characteristic function form"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Cooperative_game_theory" title="Cooperative game theory">Cooperative game theory</a></div> <p>In cooperative game theory the characteristic function lists the payoff of each coalition. The origin of this formulation is in John von Neumann and Oskar Morgenstern's book.<sup class="noprint Inline-Template Template-Fact" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Citation_needed" title="Wikipedia:Citation needed"><span title="This claim needs references to reliable sources. (May 2024)">citation needed</span></a></i>]</sup> </p><p>Formally, a characteristic function is a function <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle v:2^{N}\to \mathbb {R} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>v</mi> <mo>:</mo> <msup> <mn>2</mn> <mrow class="MJX-TeXAtom-ORD"> <mi>N</mi> </mrow> </msup> <mo stretchy="false">→</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">R</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle v:2^{N}\to \mathbb {R} }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/942f22d1156193e30cbe399bfe2fdd160d0d0419" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:11.211ex; height:2.676ex;" alt="{\displaystyle v:2^{N}\to \mathbb {R} }"></span> <sup id="cite_ref-52" class="reference"><a href="#cite_note-52"><span class="cite-bracket">[</span>51<span class="cite-bracket">]</span></a></sup> from the set of all possible coalitions of players to a set of payments, and also satisfies <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle v(\emptyset )=0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>v</mi> <mo stretchy="false">(</mo> <mi mathvariant="normal">∅</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle v(\emptyset )=0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3b4ab6cb7570d8cbaa5dcc5503b5a21327ed4997" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:8.36ex; height:2.843ex;" alt="{\displaystyle v(\emptyset )=0}"></span>. The function describes how much collective payoff a set of players can gain by forming a coalition. </p> <div class="mw-heading mw-heading3"><h3 id="Alternative_game_representations">Alternative game representations</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Game_theory&action=edit&section=23" title="Edit section: Alternative game representations"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">See also: <a href="/wiki/Succinct_game" title="Succinct game">Succinct game</a></div> <p>Alternative game representation forms are used for some subclasses of games or adjusted to the needs of interdisciplinary research.<sup id="cite_ref-53" class="reference"><a href="#cite_note-53"><span class="cite-bracket">[</span>52<span class="cite-bracket">]</span></a></sup> In addition to classical game representations, some of the alternative representations also encode time related aspects. </p> <table class="wikitable sortable"> <tbody><tr> <th>Name </th> <th>Year </th> <th>Means </th> <th><a href="#Game_types">Type of games</a> </th> <th>Time </th></tr> <tr> <td><a href="/wiki/Congestion_game" title="Congestion game">Congestion game</a><sup id="cite_ref-54" class="reference"><a href="#cite_note-54"><span class="cite-bracket">[</span>53<span class="cite-bracket">]</span></a></sup> </td> <td>1973 </td> <td>functions </td> <td>subset of n-person games, simultaneous moves </td> <td>No </td></tr> <tr> <td>Sequential form<sup id="cite_ref-55" class="reference"><a href="#cite_note-55"><span class="cite-bracket">[</span>54<span class="cite-bracket">]</span></a></sup> </td> <td>1994 </td> <td>matrices </td> <td>2-person games of imperfect information </td> <td>No </td></tr> <tr> <td>Timed games<sup id="cite_ref-56" class="reference"><a href="#cite_note-56"><span class="cite-bracket">[</span>55<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-57" class="reference"><a href="#cite_note-57"><span class="cite-bracket">[</span>56<span class="cite-bracket">]</span></a></sup> </td> <td>1994 </td> <td>functions </td> <td>2-person games </td> <td>Yes </td></tr> <tr> <td>Gala<sup id="cite_ref-58" class="reference"><a href="#cite_note-58"><span class="cite-bracket">[</span>57<span class="cite-bracket">]</span></a></sup> </td> <td>1997 </td> <td><a href="/wiki/First-order_logic" title="First-order logic">logic</a> </td> <td>n-person games of imperfect information </td> <td>No </td></tr> <tr> <td><a href="/wiki/Graphical_game_theory" title="Graphical game theory">Graphical games</a><sup id="cite_ref-59" class="reference"><a href="#cite_note-59"><span class="cite-bracket">[</span>58<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-60" class="reference"><a href="#cite_note-60"><span class="cite-bracket">[</span>59<span class="cite-bracket">]</span></a></sup> </td> <td>2001 </td> <td>graphs, functions </td> <td>n-person games, simultaneous moves </td> <td>No </td></tr> <tr> <td>Local effect games<sup id="cite_ref-61" class="reference"><a href="#cite_note-61"><span class="cite-bracket">[</span>60<span class="cite-bracket">]</span></a></sup> </td> <td>2003 </td> <td>functions </td> <td>subset of n-person games, simultaneous moves </td> <td>No </td></tr> <tr> <td><a href="/wiki/Game_description_language" class="mw-redirect" title="Game description language">GDL</a><sup id="cite_ref-62" class="reference"><a href="#cite_note-62"><span class="cite-bracket">[</span>61<span class="cite-bracket">]</span></a></sup> </td> <td>2005 </td> <td><a href="/wiki/First-order_logic" title="First-order logic">logic</a> </td> <td>deterministic n-person games, simultaneous moves </td> <td>No </td></tr> <tr> <td>Game Petri-nets<sup id="cite_ref-63" class="reference"><a href="#cite_note-63"><span class="cite-bracket">[</span>62<span class="cite-bracket">]</span></a></sup> </td> <td>2006 </td> <td><a href="/wiki/Petri_net" title="Petri net">Petri net</a> </td> <td>deterministic n-person games, simultaneous moves </td> <td>No </td></tr> <tr> <td>Continuous games<sup id="cite_ref-64" class="reference"><a href="#cite_note-64"><span class="cite-bracket">[</span>63<span class="cite-bracket">]</span></a></sup> </td> <td>2007 </td> <td>functions </td> <td>subset of 2-person games of imperfect information </td> <td>Yes </td></tr> <tr> <td>PNSI<sup id="cite_ref-65" class="reference"><a href="#cite_note-65"><span class="cite-bracket">[</span>64<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-66" class="reference"><a href="#cite_note-66"><span class="cite-bracket">[</span>65<span class="cite-bracket">]</span></a></sup> </td> <td>2008 </td> <td><a href="/wiki/Petri_net" title="Petri net">Petri net</a> </td> <td>n-person games of imperfect information </td> <td>Yes </td></tr> <tr> <td>Action graph games<sup id="cite_ref-67" class="reference"><a href="#cite_note-67"><span class="cite-bracket">[</span>66<span class="cite-bracket">]</span></a></sup> </td> <td>2012 </td> <td>graphs, functions </td> <td>n-person games, simultaneous moves </td> <td>No </td></tr></tbody></table> <div class="mw-heading mw-heading2"><h2 id="General_and_applied_uses">General and applied uses</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Game_theory&action=edit&section=24" title="Edit section: General and applied uses"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>As a method of <a href="/wiki/Applied_mathematics" title="Applied mathematics">applied mathematics</a>, game theory has been used to study a wide variety of human and animal behaviors. It was initially developed in <a href="/wiki/Economics" title="Economics">economics</a> to understand a large collection of economic behaviors, including behaviors of firms, markets, and consumers. The first use of game-theoretic analysis was by <a href="/wiki/Antoine_Augustin_Cournot" title="Antoine Augustin Cournot">Antoine Augustin Cournot</a> in 1838 with his solution of the <a href="/wiki/Cournot_competition" title="Cournot competition">Cournot duopoly</a>. The use of game theory in the social sciences has expanded, and game theory has been applied to political, sociological, and psychological behaviors as well.<sup id="cite_ref-Larson_68-0" class="reference"><a href="#cite_note-Larson-68"><span class="cite-bracket">[</span>67<span class="cite-bracket">]</span></a></sup> </p><p>Although pre-twentieth-century <a href="/wiki/Natural_history" title="Natural history">naturalists</a> such as <a href="/wiki/Charles_Darwin" title="Charles Darwin">Charles Darwin</a> made game-theoretic kinds of statements, the use of game-theoretic analysis in biology began with <a href="/wiki/Ronald_Fisher" title="Ronald Fisher">Ronald Fisher</a>'s studies of animal behavior during the 1930s. This work predates the name "game theory", but it shares many important features with this field. The developments in economics were later applied to biology largely by John Maynard Smith in his 1982 book <i><a href="/wiki/Evolution_and_the_Theory_of_Games" title="Evolution and the Theory of Games">Evolution and the Theory of Games</a></i>.<sup id="cite_ref-69" class="reference"><a href="#cite_note-69"><span class="cite-bracket">[</span>68<span class="cite-bracket">]</span></a></sup> </p><p>In addition to being used to describe, predict, and explain behavior, game theory has also been used to develop theories of ethical or normative behavior and to <a href="/wiki/Decision_theory#Normative_and_descriptive_decision_theory" title="Decision theory">prescribe</a> such behavior.<sup id="cite_ref-Camerer2003_70-0" class="reference"><a href="#cite_note-Camerer2003-70"><span class="cite-bracket">[</span>69<span class="cite-bracket">]</span></a></sup> In <a href="/wiki/Economics_and_philosophy" class="mw-redirect" title="Economics and philosophy">economics and philosophy</a>, scholars have applied game theory to help in the understanding of good or proper behavior. Game-theoretic approaches have also been suggested in the <a href="/wiki/Philosophy_of_language" title="Philosophy of language">philosophy of language</a> and <a href="/wiki/Philosophy_of_science" title="Philosophy of science">philosophy of science</a>.<sup id="cite_ref-71" class="reference"><a href="#cite_note-71"><span class="cite-bracket">[</span>70<span class="cite-bracket">]</span></a></sup> Game-theoretic arguments of this type can be found as far back as <a href="/wiki/Plato" title="Plato">Plato</a>.<sup id="cite_ref-72" class="reference"><a href="#cite_note-72"><span class="cite-bracket">[</span>71<span class="cite-bracket">]</span></a></sup> An alternative version of game theory, called <a href="/wiki/Chemical_game_theory" title="Chemical game theory">chemical game theory</a>, represents the player's choices as metaphorical chemical reactant molecules called "knowlecules".<sup id="cite_ref-73" class="reference"><a href="#cite_note-73"><span class="cite-bracket">[</span>72<span class="cite-bracket">]</span></a></sup>  Chemical game theory then calculates the outcomes as equilibrium solutions to a system of chemical reactions. </p> <div class="mw-heading mw-heading3"><h3 id="Description_and_modeling">Description and modeling</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Game_theory&action=edit&section=25" title="Edit section: Description and modeling"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:Centipede_game.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/9/96/Centipede_game.svg/280px-Centipede_game.svg.png" decoding="async" width="280" height="93" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/9/96/Centipede_game.svg/420px-Centipede_game.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/9/96/Centipede_game.svg/560px-Centipede_game.svg.png 2x" data-file-width="2496" data-file-height="832" /></a><figcaption>A four-stage <a href="/wiki/Centipede_game" title="Centipede game">centipede game</a></figcaption></figure> <p>The primary use of game theory is to describe and <a href="/wiki/Conceptual_model#Economic_models" title="Conceptual model">model</a> how human populations behave.<sup class="noprint Inline-Template Template-Fact" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Citation_needed" title="Wikipedia:Citation needed"><span title="This claim needs references to reliable sources. (November 2019)">citation needed</span></a></i>]</sup> Some<sup class="noprint Inline-Template" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Manual_of_Style/Words_to_watch#Unsupported_attributions" title="Wikipedia:Manual of Style/Words to watch"><span title="The material near this tag possibly uses too-vague attribution or weasel words. (July 2012)">who?</span></a></i>]</sup> scholars believe that by finding the equilibria of games they can predict how actual human populations will behave when confronted with situations analogous to the game being studied. This particular view of game theory has been criticized. It is argued that the assumptions made by game theorists are often violated when applied to real-world situations. Game theorists usually assume players act rationally, but in practice, human rationality and/or behavior often deviates from the model of rationality as used in game theory. Game theorists respond by comparing their assumptions to those used in <a href="/wiki/Physics" title="Physics">physics</a>. Thus while their assumptions do not always hold, they can treat game theory as a reasonable scientific <a href="/wiki/Idealization_(science_philosophy)" class="mw-redirect" title="Idealization (science philosophy)">ideal</a> akin to the models used by <a href="/wiki/Physicist" title="Physicist">physicists</a>. However, empirical work has shown that in some classic games, such as the <a href="/wiki/Centipede_game" title="Centipede game">centipede game</a>, <a href="/wiki/Guess_2/3_of_the_average" title="Guess 2/3 of the average">guess 2/3 of the average</a> game, and the <a href="/wiki/Dictator_game" title="Dictator game">dictator game</a>, people regularly do not play Nash equilibria. There is an ongoing debate regarding the importance of these experiments and whether the analysis of the experiments fully captures all aspects of the relevant situation.<sup id="cite_ref-75" class="reference"><a href="#cite_note-75"><span class="cite-bracket">[</span>b<span class="cite-bracket">]</span></a></sup> </p><p>Some game theorists, following the work of John Maynard Smith and <a href="/wiki/George_R._Price" title="George R. Price">George R. Price</a>, have turned to evolutionary game theory in order to resolve these issues. These models presume either no rationality or <a href="/wiki/Bounded_rationality" title="Bounded rationality">bounded rationality</a> on the part of players. Despite the name, evolutionary game theory does not necessarily presume <a href="/wiki/Natural_selection" title="Natural selection">natural selection</a> in the biological sense. Evolutionary game theory includes both biological as well as cultural evolution and also models of individual learning (for example, <a href="/wiki/Fictitious_play" title="Fictitious play">fictitious play</a> dynamics). </p> <div class="mw-heading mw-heading3"><h3 id="Prescriptive_or_normative_analysis">Prescriptive or normative analysis</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Game_theory&action=edit&section=26" title="Edit section: Prescriptive or normative analysis"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <table id="Payoff_matrix" style="background:white; float: right; clear:right; text-align:center;" align="right" cellspacing="0" cellpadding="8" width="225"> <tbody><tr> <td style="width:33%;"> </td> <td style="width:33%; border-bottom: solid black 1px;">Cooperate </td> <td style="width:33%; border-bottom: solid black 1px;">Defect </td></tr> <tr> <td style="border-right: solid black 1px; text-align: right;">Cooperate </td> <td style="border-right: solid black 1px; border-bottom: solid black 1px; background:white; font-size:120%; white-space:nowrap;">-1, −1 </td> <td style="border-right: solid black 1px; border-bottom: solid black 1px; background:white; font-size:120%; white-space:nowrap;">-10, 0 </td></tr> <tr> <td style="border-right: solid black 1px; text-align: right;">Defect </td> <td style="border-right: solid black 1px; border-bottom: solid black 1px; background:white; font-size:120%; white-space:nowrap;">0, −10 </td> <td style="border-right: solid black 1px; border-bottom: solid black 1px; background:white; font-size:120%; white-space:nowrap;">-5, −5 </td></tr> <tr> <td style="font-size: 90%;" colspan="3"><i>The prisoner's dilemma</i> </td></tr></tbody></table> <p>Some scholars see game theory not as a predictive tool for the behavior of human beings, but as a suggestion for how people ought to behave. Since a strategy, corresponding to a Nash equilibrium of a game constitutes one's <a href="/wiki/Best_response" title="Best response">best response</a> to the actions of the other players – provided they are in (the same) Nash equilibrium – playing a strategy that is part of a Nash equilibrium seems appropriate. This normative use of game theory has also come under criticism.<sup id="cite_ref-76" class="reference"><a href="#cite_note-76"><span class="cite-bracket">[</span>74<span class="cite-bracket">]</span></a></sup> </p><p><span class="anchor" id="Economics"></span> </p> <div class="mw-heading mw-heading3"><h3 id="Economics">Economics</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Game_theory&action=edit&section=27" title="Edit section: Economics"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Game theory is a major method used in mathematical economics and business for <a href="/wiki/Economic_model" title="Economic model">modeling</a> competing behaviors of interacting <a href="/wiki/Agent_(economics)" title="Agent (economics)">agents</a>.<sup id="cite_ref-77" class="reference"><a href="#cite_note-77"><span class="cite-bracket">[</span>c<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-78" class="reference"><a href="#cite_note-78"><span class="cite-bracket">[</span>75<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-79" class="reference"><a href="#cite_note-79"><span class="cite-bracket">[</span>76<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-80" class="reference"><a href="#cite_note-80"><span class="cite-bracket">[</span>77<span class="cite-bracket">]</span></a></sup> Applications include a wide array of economic phenomena and approaches, such as <a href="/wiki/Auction" title="Auction">auctions</a>, <a href="/wiki/Bargaining" title="Bargaining">bargaining</a>, <a href="/wiki/Mergers_and_acquisitions" title="Mergers and acquisitions">mergers and acquisitions</a> pricing,<sup id="cite_ref-GT-A-E-00_81-0" class="reference"><a href="#cite_note-GT-A-E-00-81"><span class="cite-bracket">[</span>78<span class="cite-bracket">]</span></a></sup> <a href="/wiki/Fair_division" title="Fair division">fair division</a>, <a href="/wiki/Duopoly" title="Duopoly">duopolies</a>, <a href="/wiki/Oligopoly" title="Oligopoly">oligopolies</a>, <a href="/wiki/Social_network" title="Social network">social network</a> formation, <a href="/wiki/Agent-based_computational_economics" title="Agent-based computational economics">agent-based computational economics</a>,<sup id="cite_ref-82" class="reference"><a href="#cite_note-82"><span class="cite-bracket">[</span>79<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-83" class="reference"><a href="#cite_note-83"><span class="cite-bracket">[</span>80<span class="cite-bracket">]</span></a></sup> <a href="/wiki/General_equilibrium" class="mw-redirect" title="General equilibrium">general equilibrium</a>, mechanism design,<sup id="cite_ref-84" class="reference"><a href="#cite_note-84"><span class="cite-bracket">[</span>81<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-85" class="reference"><a href="#cite_note-85"><span class="cite-bracket">[</span>82<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-86" class="reference"><a href="#cite_note-86"><span class="cite-bracket">[</span>83<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-nisanronen2001_87-0" class="reference"><a href="#cite_note-nisanronen2001-87"><span class="cite-bracket">[</span>84<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-nisan2007_88-0" class="reference"><a href="#cite_note-nisan2007-88"><span class="cite-bracket">[</span>85<span class="cite-bracket">]</span></a></sup> and <a href="/wiki/Voting_system" class="mw-redirect" title="Voting system">voting systems</a>;<sup id="cite_ref-89" class="reference"><a href="#cite_note-89"><span class="cite-bracket">[</span>86<span class="cite-bracket">]</span></a></sup> and across such broad areas as experimental economics,<sup id="cite_ref-90" class="reference"><a href="#cite_note-90"><span class="cite-bracket">[</span>87<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-91" class="reference"><a href="#cite_note-91"><span class="cite-bracket">[</span>88<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-92" class="reference"><a href="#cite_note-92"><span class="cite-bracket">[</span>89<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-93" class="reference"><a href="#cite_note-93"><span class="cite-bracket">[</span>90<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-94" class="reference"><a href="#cite_note-94"><span class="cite-bracket">[</span>91<span class="cite-bracket">]</span></a></sup> <a href="/wiki/Behavioral_game_theory" title="Behavioral game theory">behavioral economics</a>,<sup id="cite_ref-95" class="reference"><a href="#cite_note-95"><span class="cite-bracket">[</span>92<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-96" class="reference"><a href="#cite_note-96"><span class="cite-bracket">[</span>93<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-97" class="reference"><a href="#cite_note-97"><span class="cite-bracket">[</span>94<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-98" class="reference"><a href="#cite_note-98"><span class="cite-bracket">[</span>95<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-99" class="reference"><a href="#cite_note-99"><span class="cite-bracket">[</span>96<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-100" class="reference"><a href="#cite_note-100"><span class="cite-bracket">[</span>97<span class="cite-bracket">]</span></a></sup> <a href="/wiki/Information_economics" title="Information economics">information economics</a>,<sup id="cite_ref-r7a_45-1" class="reference"><a href="#cite_note-r7a-45"><span class="cite-bracket">[</span>44<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-r7b_46-1" class="reference"><a href="#cite_note-r7b-46"><span class="cite-bracket">[</span>45<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-r7c_47-1" class="reference"><a href="#cite_note-r7c-47"><span class="cite-bracket">[</span>46<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-r7d_48-1" class="reference"><a href="#cite_note-r7d-48"><span class="cite-bracket">[</span>47<span class="cite-bracket">]</span></a></sup> <a href="/wiki/Industrial_organization" title="Industrial organization">industrial organization</a>,<sup id="cite_ref-101" class="reference"><a href="#cite_note-101"><span class="cite-bracket">[</span>98<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-102" class="reference"><a href="#cite_note-102"><span class="cite-bracket">[</span>99<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-103" class="reference"><a href="#cite_note-103"><span class="cite-bracket">[</span>100<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-104" class="reference"><a href="#cite_note-104"><span class="cite-bracket">[</span>101<span class="cite-bracket">]</span></a></sup> and <a href="/wiki/Political_economy" title="Political economy">political economy</a>.<sup id="cite_ref-105" class="reference"><a href="#cite_note-105"><span class="cite-bracket">[</span>102<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-106" class="reference"><a href="#cite_note-106"><span class="cite-bracket">[</span>103<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-107" class="reference"><a href="#cite_note-107"><span class="cite-bracket">[</span>104<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-r7c_47-2" class="reference"><a href="#cite_note-r7c-47"><span class="cite-bracket">[</span>46<span class="cite-bracket">]</span></a></sup> </p><p>This research usually focuses on particular sets of strategies known as <a href="/wiki/Solution_concept" title="Solution concept">"solution concepts" or "equilibria"</a>. A common assumption is that players act rationally. In non-cooperative games, the most famous of these is the Nash equilibrium. A set of strategies is a Nash equilibrium if each represents a best response to the other strategies. If all the players are playing the strategies in a Nash equilibrium, they have no unilateral incentive to deviate, since their strategy is the best they can do given what others are doing.<sup id="cite_ref-GT-F-R-09_108-0" class="reference"><a href="#cite_note-GT-F-R-09-108"><span class="cite-bracket">[</span>105<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-GT-F-R-10_109-0" class="reference"><a href="#cite_note-GT-F-R-10-109"><span class="cite-bracket">[</span>106<span class="cite-bracket">]</span></a></sup> </p><p>The payoffs of the game are generally taken to represent the <a href="/wiki/Utility" title="Utility">utility</a> of individual players. </p><p>A prototypical paper on game theory in economics begins by presenting a game that is an abstraction of a particular economic situation. One or more solution concepts are chosen, and the author demonstrates which strategy sets in the presented game are equilibria of the appropriate type. Economists and business professors suggest two primary uses (noted above): <i>descriptive</i> and <i><a href="/wiki/Decision_theory#Normative_and_descriptive_decision_theory" title="Decision theory">prescriptive</a></i>.<sup id="cite_ref-Camerer2003_70-1" class="reference"><a href="#cite_note-Camerer2003-70"><span class="cite-bracket">[</span>69<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading4"><h4 id="Managerial_economics">Managerial economics</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Game_theory&action=edit&section=28" title="Edit section: Managerial economics"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Game theory also has an extensive use in a specific branch or stream of economics – <a href="/wiki/Managerial_economics" title="Managerial economics">Managerial Economics</a>. One important usage of it in the field of managerial economics is in analyzing strategic interactions between firms.<sup id="cite_ref-110" class="reference"><a href="#cite_note-110"><span class="cite-bracket">[</span>107<span class="cite-bracket">]</span></a></sup> For example, firms may be competing in a market with limited resources, and game theory can help managers understand how their decisions impact their competitors and the overall market outcomes. Game theory can also be used to analyze cooperation between firms, such as in forming strategic alliances or joint ventures. Another use of game theory in managerial economics is in analyzing pricing strategies. For example, firms may use game theory to determine the optimal <a href="/wiki/Pricing_strategy" class="mw-redirect" title="Pricing strategy">pricing strategy</a> based on how they expect their competitors to respond to their pricing decisions. Overall, game theory serves as a useful tool for analyzing strategic interactions and decision making in the context of managerial economics. </p> <div class="mw-heading mw-heading3"><h3 id="Business">Business</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Game_theory&action=edit&section=29" title="Edit section: Business"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The <a href="/wiki/Chartered_Institute_of_Procurement_%26_Supply" title="Chartered Institute of Procurement & Supply">Chartered Institute of Procurement & Supply</a> (CIPS) promotes knowledge and use of game theory within the context of business <a href="/wiki/Procurement" title="Procurement">procurement</a>.<sup id="cite_ref-111" class="reference"><a href="#cite_note-111"><span class="cite-bracket">[</span>108<span class="cite-bracket">]</span></a></sup> CIPS and TWS Partners have conducted a series of surveys designed to explore the understanding, awareness and application of game theory among <a href="/wiki/Procurement" title="Procurement">procurement</a> professionals. Some of the main findings in their third annual survey (2019) include: </p> <ul><li>application of game theory to procurement activity has increased – at the time it was at 19% across all survey respondents</li> <li>65% of participants predict that use of game theory applications will grow</li> <li>70% of respondents say that they have "only a basic or a below basic understanding" of game theory</li> <li>20% of participants had undertaken <a href="/wiki/On-the-job_training" title="On-the-job training">on-the-job training</a> in game theory</li> <li>50% of respondents said that new or improved software solutions were desirable</li> <li>90% of respondents said that they do not have the software they need for their work.<sup id="cite_ref-112" class="reference"><a href="#cite_note-112"><span class="cite-bracket">[</span>109<span class="cite-bracket">]</span></a></sup></li></ul> <div class="mw-heading mw-heading3"><h3 id="Project_management">Project management</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Game_theory&action=edit&section=30" title="Edit section: Project management"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Sensible decision-making is critical for the success of projects. In project management, game theory is used to model the decision-making process of players, such as investors, project managers, contractors, sub-contractors, governments and customers. Quite often, these players have competing interests, and sometimes their interests are directly detrimental to other players, making project management scenarios well-suited to be modeled by game theory. </p><p>Piraveenan (2019)<sup id="cite_ref-Piraveenan_2019_113-0" class="reference"><a href="#cite_note-Piraveenan_2019-113"><span class="cite-bracket">[</span>110<span class="cite-bracket">]</span></a></sup> in his review provides several examples where game theory is used to model project management scenarios. For instance, an investor typically has several investment options, and each option will likely result in a different project, and thus one of the investment options has to be chosen before the project charter can be produced. Similarly, any large project involving subcontractors, for instance, a construction project, has a complex interplay between the main contractor (the project manager) and subcontractors, or among the subcontractors themselves, which typically has several decision points. For example, if there is an ambiguity in the contract between the contractor and subcontractor, each must decide how hard to push their case without jeopardizing the whole project, and thus their own stake in it. Similarly, when projects from competing organizations are launched, the marketing personnel have to decide what is the best timing and strategy to market the project, or its resultant product or service, so that it can gain maximum traction in the face of competition. In each of these scenarios, the required decisions depend on the decisions of other players who, in some way, have competing interests to the interests of the decision-maker, and thus can ideally be modeled using game theory. </p><p>Piraveenan<sup id="cite_ref-Piraveenan_2019_113-1" class="reference"><a href="#cite_note-Piraveenan_2019-113"><span class="cite-bracket">[</span>110<span class="cite-bracket">]</span></a></sup> summarizes that two-player games are predominantly used to model project management scenarios, and based on the identity of these players, five distinct types of games are used in project management. </p> <ul><li>Government-sector–private-sector games (games that model <a href="/wiki/Public%E2%80%93private_partnership" title="Public–private partnership">public–private partnerships</a>)</li> <li>Contractor–contractor games</li> <li>Contractor–subcontractor games</li> <li>Subcontractor–subcontractor games</li> <li>Games involving other players</li></ul> <p>In terms of types of games, both cooperative as well as non-cooperative, normal-form as well as extensive-form, and zero-sum as well as non-zero-sum are used to model various project management scenarios. </p> <div class="mw-heading mw-heading3"><h3 id="Political_science">Political science</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Game_theory&action=edit&section=31" title="Edit section: Political science"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1246091330"><style data-mw-deduplicate="TemplateStyles:r1202158006">.mw-parser-output .law-sidebar .sidebar-heading{background:#aaddff;color:#000}.mw-parser-output .law-sidebar .sidebar-above{font-weight:normal}.mw-parser-output .law-sidebar .sidebar-below{padding:0.4em;border-top:1px #aaa solid;font-weight:normal;font-size:smaller}</style><table class="sidebar nomobile nowraplinks hlist law-sidebar"><tbody><tr><th class="sidebar-title"><a href="/wiki/Conflict_resolution" title="Conflict resolution">Conflict resolution</a></th></tr><tr><th class="sidebar-heading"> <a href="/wiki/Nonviolence" title="Nonviolence">Nonviolence</a></th></tr><tr><td class="sidebar-content"> <ul><li><a href="/wiki/Arbitration" title="Arbitration">Arbitration</a></li> <li><a href="/wiki/Auction" title="Auction">Auction</a></li> <li><a href="/wiki/Conciliation" title="Conciliation">Conciliation</a></li> <li><a href="/wiki/Law" title="Law">Law</a> <ul><li><a href="/wiki/Dispute_resolution" title="Dispute resolution">Dispute resolution</a></li> <li><a href="/wiki/Rule_of_law" title="Rule of law">Rule of law</a></li> <li><a href="/wiki/Collaborative_law" title="Collaborative law">Collaborative</a></li></ul></li> <li><a href="/wiki/Mediation" title="Mediation">Mediation</a> <ul><li><a href="/wiki/Party-directed_mediation" title="Party-directed mediation">Party-directed</a></li></ul></li> <li><a href="/wiki/Nonviolent_Communication" title="Nonviolent Communication">Nonviolent Communication</a></li> <li><a href="/wiki/Pacifism" title="Pacifism">Pacifism</a></li> <li><a href="/wiki/Negotiation" title="Negotiation">Negotiation</a></li> <li><a href="/wiki/Speaking_truth_to_power" title="Speaking truth to power">Speaking truth to power</a></li></ul></td> </tr><tr><th class="sidebar-heading"> Workplace</th></tr><tr><td class="sidebar-content"> <ul><li><a href="/wiki/Conflict_management" title="Conflict management">Conflict management</a></li></ul></td> </tr><tr><th class="sidebar-heading"> <a href="/wiki/Violence" title="Violence">Violence</a></th></tr><tr><td class="sidebar-content"> <ul><li><a href="/wiki/Communal_violence" title="Communal violence">Communal violence</a></li> <li><a href="/wiki/Conflict_escalation" title="Conflict escalation">Conflict escalation</a></li> <li><a href="/wiki/De-escalation" title="De-escalation">De-escalation</a></li> <li><a href="/wiki/Just_war_theory" title="Just war theory">Just war theory</a></li> <li><a href="/wiki/War" title="War">War</a> <ul><li><a href="/wiki/War_studies" title="War studies">studies</a></li></ul></li></ul></td> </tr><tr><th class="sidebar-heading"> <a href="/wiki/International_relations" title="International relations">International relations</a></th></tr><tr><td class="sidebar-content"> <ul><li><a href="/wiki/Appeasement" title="Appeasement">Appeasement</a></li> <li><a href="/wiki/Armistice" title="Armistice">Armistice</a></li> <li><a href="/wiki/Brinkmanship" title="Brinkmanship">Brinkmanship</a></li> <li><a href="/wiki/Ceasefire" title="Ceasefire">Ceasefire</a></li> <li><a href="/wiki/Diplomacy" title="Diplomacy">Diplomacy</a></li> <li><a href="/wiki/Deterrence_theory" title="Deterrence theory">Deterrence</a></li> <li><a href="/wiki/Multilateralism" title="Multilateralism">Multilateralism</a></li></ul></td> </tr><tr><th class="sidebar-heading"> Nuclear</th></tr><tr><td class="sidebar-content"> <ul><li><a href="/wiki/Nuclear_warfare" title="Nuclear warfare">Nuclear warfare</a></li> <li><a href="/wiki/Nuclear_blackmail" title="Nuclear blackmail">Nuclear blackmail</a></li> <li><a href="/wiki/Mutual_assured_destruction" title="Mutual assured destruction">Mutual assured destruction</a></li> <li><a href="/wiki/Nuclear_disarmament" title="Nuclear disarmament">Nuclear disarmament</a></li> <li><a href="/wiki/Nuclear_proliferation" title="Nuclear proliferation">Nuclear proliferation</a></li></ul></td> </tr><tr><th class="sidebar-heading"> Other</th></tr><tr><td class="sidebar-content"> <ul><li><a href="/wiki/Alternative_dispute_resolution" title="Alternative dispute resolution">Alternative dispute resolution</a></li> <li><a href="/wiki/Anti-war_movement" title="Anti-war movement">Anti-war movement</a></li> <li><a href="/wiki/Conflict_avoidance" title="Conflict avoidance">Conflict avoidance</a></li> <li><a href="/wiki/Conflict_continuum" title="Conflict continuum">Conflict continuum</a></li> <li><a href="/wiki/Conflict_style_inventory" title="Conflict style inventory">Conflict style inventory</a></li> <li><a href="/wiki/Democracy" title="Democracy">Democracy</a></li> <li><a href="/wiki/Family_therapy" title="Family therapy">Family therapy</a></li> <li><a href="/wiki/Forum_(alternative_dispute_resolution)" title="Forum (alternative dispute resolution)">Forum (alternative dispute resolution)</a></li> <li><a class="mw-selflink selflink">Game theory</a> <ul><li><a href="/wiki/Prisoner%27s_dilemma" title="Prisoner's dilemma">Prisoner's dilemma</a></li> <li><a href="/wiki/Paradox_of_tolerance" title="Paradox of tolerance">Paradox of tolerance</a></li></ul></li> <li><a href="/wiki/Liaison_officer" title="Liaison officer">Liaison officer</a></li> <li><a href="/wiki/Non-aggression_principle" title="Non-aggression principle">Non-aggression principle</a></li> <li><a href="/wiki/Peace_and_conflict_studies" title="Peace and conflict studies">Peace and conflict studies</a></li> <li><a href="/wiki/Peace_process" title="Peace process">Peace process</a></li> <li><a href="/wiki/Peace_treaty" title="Peace treaty">Peace treaty</a></li> <li><a href="/wiki/Peacebuilding" title="Peacebuilding">Peacebuilding</a></li> <li><a href="/wiki/Peacemaking" title="Peacemaking">Peacemaking</a></li> <li><a href="/wiki/Rule_of_man" title="Rule of man">Rule of man</a></li> <li><a href="/wiki/Track_II_diplomacy" title="Track II diplomacy">Track II diplomacy</a></li></ul></td> </tr><tr><td class="sidebar-navbar"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1239400231"><div class="navbar plainlinks hlist navbar-mini"><ul><li class="nv-view"><a href="/wiki/Template:Conflict_resolution_sidebar" title="Template:Conflict resolution sidebar"><abbr title="View this template">v</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:Conflict_resolution_sidebar" title="Template talk:Conflict resolution sidebar"><abbr title="Discuss this template">t</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:EditPage/Template:Conflict_resolution_sidebar" title="Special:EditPage/Template:Conflict resolution sidebar"><abbr title="Edit this template">e</abbr></a></li></ul></div></td></tr></tbody></table> <p>The application of game theory to <a href="/wiki/Political_science" title="Political science">political science</a> is focused in the overlapping areas of <a href="/wiki/Fair_division" title="Fair division">fair division</a>, <a href="/wiki/Political_economy" title="Political economy">political economy</a>, <a href="/wiki/Public_choice" title="Public choice">public choice</a>, <a href="/wiki/War%27s_inefficiency_puzzle" class="mw-redirect" title="War's inefficiency puzzle">war bargaining</a>, <a href="/wiki/Positive_political_theory" title="Positive political theory">positive political theory</a>, and <a href="/wiki/Social_choice_theory" title="Social choice theory">social choice theory</a>. In each of these areas, researchers have developed game-theoretic models in which the players are often voters, states, special interest groups, and politicians.<sup id="cite_ref-114" class="reference"><a href="#cite_note-114"><span class="cite-bracket">[</span>111<span class="cite-bracket">]</span></a></sup> </p><p>Early examples of game theory applied to political science are provided by <a href="/wiki/Anthony_Downs" title="Anthony Downs">Anthony Downs</a>. In his 1957 book <i><a href="/wiki/An_Economic_Theory_of_Democracy" title="An Economic Theory of Democracy">An Economic Theory of Democracy</a></i>,<sup id="cite_ref-FOOTNOTEDowns1957_115-0" class="reference"><a href="#cite_note-FOOTNOTEDowns1957-115"><span class="cite-bracket">[</span>112<span class="cite-bracket">]</span></a></sup> he applies the <a href="/wiki/Hotelling%27s_law" title="Hotelling's law">Hotelling firm location model</a> to the political process. In the Downsian model, political candidates commit to ideologies on a one-dimensional policy space. Downs first shows how the political candidates will converge to the ideology preferred by the median voter if voters are fully informed, but then argues that voters choose to remain rationally ignorant which allows for candidate divergence. Game theory was applied in 1962 to the <a href="/wiki/Cuban_Missile_Crisis" title="Cuban Missile Crisis">Cuban Missile Crisis</a> during the presidency of John F. Kennedy.<sup id="cite_ref-116" class="reference"><a href="#cite_note-116"><span class="cite-bracket">[</span>113<span class="cite-bracket">]</span></a></sup> </p><p>It has also been proposed that game theory explains the stability of any form of political government. Taking the simplest case of a monarchy, for example, the king, being only one person, does not and cannot maintain his authority by personally exercising physical control over all or even any significant number of his subjects. Sovereign control is instead explained by the recognition by each citizen that all other citizens expect each other to view the king (or other established government) as the person whose orders will be followed. Coordinating communication among citizens to replace the sovereign is effectively barred, since conspiracy to replace the sovereign is generally punishable as a crime.<sup id="cite_ref-117" class="reference"><a href="#cite_note-117"><span class="cite-bracket">[</span>114<span class="cite-bracket">]</span></a></sup> Thus, in a process that can be modeled by variants of the prisoner's dilemma, during periods of stability no citizen will find it rational to move to replace the sovereign, even if all the citizens know they would be better off if they were all to act collectively.<sup class="noprint Inline-Template Template-Fact" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Citation_needed" title="Wikipedia:Citation needed"><span title="This claim needs references to reliable sources. (July 2024)">citation needed</span></a></i>]</sup> </p><p>A game-theoretic explanation for <a href="/wiki/Democratic_peace_theory" title="Democratic peace theory">democratic peace</a> is that public and open debate in democracies sends clear and reliable information regarding their intentions to other states. In contrast, it is difficult to know the intentions of nondemocratic leaders, what effect concessions will have, and if promises will be kept. Thus there will be mistrust and unwillingness to make concessions if at least one of the parties in a dispute is a non-democracy.<sup id="cite_ref-118" class="reference"><a href="#cite_note-118"><span class="cite-bracket">[</span>115<span class="cite-bracket">]</span></a></sup> </p><p>However, game theory predicts that two countries may still go to war even if their leaders are cognizant of the costs of fighting. War may result from asymmetric information; two countries may have incentives to mis-represent the amount of military resources they have on hand, rendering them unable to settle disputes agreeably without resorting to fighting. Moreover, war may arise because of commitment problems: if two countries wish to settle a dispute via peaceful means, but each wishes to go back on the terms of that settlement, they may have no choice but to resort to warfare. Finally, war may result from issue indivisibilities.<sup id="cite_ref-119" class="reference"><a href="#cite_note-119"><span class="cite-bracket">[</span>116<span class="cite-bracket">]</span></a></sup> </p><p>Game theory could also help predict a nation's responses when there is a new rule or law to be applied to that nation. One example is Peter John Wood's (2013) research looking into what nations could do to help reduce climate change. Wood thought this could be accomplished by making treaties with other nations to reduce <a href="/wiki/Greenhouse_gas_emissions" title="Greenhouse gas emissions">greenhouse gas emissions</a>. However, he concluded that this idea could not work because it would create a prisoner's dilemma for the nations.<sup id="cite_ref-120" class="reference"><a href="#cite_note-120"><span class="cite-bracket">[</span>117<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Defence_science_and_technology">Defence science and technology</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Game_theory&action=edit&section=32" title="Edit section: Defence science and technology"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Game theory has been used extensively to model decision-making scenarios relevant to defence applications.<sup id="cite_ref-:3_121-0" class="reference"><a href="#cite_note-:3-121"><span class="cite-bracket">[</span>118<span class="cite-bracket">]</span></a></sup> Most studies that has applied game theory in defence settings are concerned with Command and Control Warfare, and can be further classified into studies dealing with (i) Resource Allocation Warfare (ii) Information Warfare (iii) Weapons Control Warfare, and (iv) Adversary Monitoring Warfare.<sup id="cite_ref-:3_121-1" class="reference"><a href="#cite_note-:3-121"><span class="cite-bracket">[</span>118<span class="cite-bracket">]</span></a></sup> Many of the problems studied are concerned with sensing and tracking, for example a surface ship trying to track a hostile submarine and the submarine trying to evade being tracked, and the interdependent decision making that takes place with regards to bearing, speed, and the sensor technology activated by both vessels. Ho et al. <sup id="cite_ref-:3_121-2" class="reference"><a href="#cite_note-:3-121"><span class="cite-bracket">[</span>118<span class="cite-bracket">]</span></a></sup> provides a concise summary of the state-of-the-art with regards to the use of game theory in defence applications and highlights the benefits and limitations of game theory in the considered scenarios. </p> <div class="mw-heading mw-heading3"><h3 id="Biology">Biology</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Game_theory&action=edit&section=33" title="Edit section: Biology"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <table id="Payoff_matrix" style="background:white; float: right; clear:right; text-align:center;" align="right" cellspacing="0" cellpadding="8" width="225"> <tbody><tr> <td style="width:33%;"> </td> <td style="width:33%; border-bottom: solid black 1px;">Hawk </td> <td style="width:33%; border-bottom: solid black 1px;">Dove </td></tr> <tr> <td style="border-right: solid black 1px; text-align: right;">Hawk </td> <td style="border-right: solid black 1px; border-bottom: solid black 1px; background:white; font-size:120%; white-space:nowrap;">20, 20 </td> <td style="border-right: solid black 1px; border-bottom: solid black 1px; background:white; font-size:120%; white-space:nowrap;">80, 40 </td></tr> <tr> <td style="border-right: solid black 1px; text-align: right;">Dove </td> <td style="border-right: solid black 1px; border-bottom: solid black 1px; background:white; font-size:120%; white-space:nowrap;">40, 80 </td> <td style="border-right: solid black 1px; border-bottom: solid black 1px; background:white; font-size:120%; white-space:nowrap;">60, 60 </td></tr> <tr> <td style="font-size: 90%;" colspan="3"><i>The <a href="/wiki/Chicken_(game)#Hawk-Dove" title="Chicken (game)">hawk-dove</a> game</i> </td></tr></tbody></table> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Evolutionary_game_theory" title="Evolutionary game theory">Evolutionary game theory</a></div> <p>Unlike those in economics, the payoffs for games in <a href="/wiki/Biology" title="Biology">biology</a> are often interpreted as corresponding to <a href="/wiki/Fitness_(biology)" title="Fitness (biology)">fitness</a>. In addition, the focus has been less on equilibria that correspond to a notion of rationality and more on ones that would be maintained by evolutionary forces. The best-known equilibrium in biology is known as the <i><a href="/wiki/Evolutionarily_stable_strategy" title="Evolutionarily stable strategy">evolutionarily stable strategy</a></i> (ESS), first introduced in (<a href="#CITEREFMaynard_SmithPrice1973">Maynard Smith & Price 1973</a>). Although its initial motivation did not involve any of the mental requirements of the Nash equilibrium, every ESS is a Nash equilibrium. </p><p>In biology, game theory has been used as a model to understand many different phenomena. It was first used to explain the evolution (and stability) of the approximate 1:1 <a href="/wiki/Sex_ratio" title="Sex ratio">sex ratios</a>. (<a href="#CITEREFFisher1930">Fisher 1930</a>) suggested that the 1:1 sex ratios are a result of evolutionary forces acting on individuals who could be seen as trying to maximize their number of grandchildren. </p><p>Additionally, biologists have used evolutionary game theory and the ESS to explain the emergence of <a href="/wiki/Animal_communication" title="Animal communication">animal communication</a>.<sup id="cite_ref-FOOTNOTEHarperMaynard_Smith2003_122-0" class="reference"><a href="#cite_note-FOOTNOTEHarperMaynard_Smith2003-122"><span class="cite-bracket">[</span>119<span class="cite-bracket">]</span></a></sup> The analysis of <a href="/wiki/Signaling_games" class="mw-redirect" title="Signaling games">signaling games</a> and <a href="/wiki/Cheap_talk" title="Cheap talk">other communication games</a> has provided insight into the evolution of communication among animals. For example, the <a href="/wiki/Mobbing_behavior" class="mw-redirect" title="Mobbing behavior">mobbing behavior</a> of many species, in which a large number of prey animals attack a larger predator, seems to be an example of spontaneous emergent organization. Ants have also been shown to exhibit feed-forward behavior akin to fashion (see <a href="/wiki/Paul_Ormerod" title="Paul Ormerod">Paul Ormerod</a>'s <i><a href="/wiki/Butterfly_Economics" title="Butterfly Economics">Butterfly Economics</a></i>). </p><p>Biologists have used the <a href="/wiki/Chicken_(game)" title="Chicken (game)">game of chicken</a> to analyze fighting behavior and territoriality.<sup id="cite_ref-123" class="reference"><a href="#cite_note-123"><span class="cite-bracket">[</span>120<span class="cite-bracket">]</span></a></sup> </p><p>According to Maynard Smith, in the preface to <i>Evolution and the Theory of Games</i>, "paradoxically, it has turned out that game theory is more readily applied to biology than to the field of economic behaviour for which it was originally designed". Evolutionary game theory has been used to explain many seemingly incongruous phenomena in nature.<sup id="cite_ref-stan-egt_124-0" class="reference"><a href="#cite_note-stan-egt-124"><span class="cite-bracket">[</span>121<span class="cite-bracket">]</span></a></sup> </p><p>One such phenomenon is known as <a href="/wiki/Altruism_in_animals" class="mw-redirect" title="Altruism in animals">biological altruism</a>. This is a situation in which an organism appears to act in a way that benefits other organisms and is detrimental to itself. This is distinct from traditional notions of altruism because such actions are not conscious, but appear to be evolutionary adaptations to increase overall fitness. Examples can be found in species ranging from vampire bats that regurgitate blood they have obtained from a night's hunting and give it to group members who have failed to feed, to worker bees that care for the queen bee for their entire lives and never mate, to <a href="/wiki/Vervet_monkey" title="Vervet monkey">vervet monkeys</a> that warn group members of a predator's approach, even when it endangers that individual's chance of survival.<sup id="cite_ref-qudzyh_125-0" class="reference"><a href="#cite_note-qudzyh-125"><span class="cite-bracket">[</span>122<span class="cite-bracket">]</span></a></sup> All of these actions increase the overall fitness of a group, but occur at a cost to the individual. </p><p>Evolutionary game theory explains this altruism with the idea of <a href="/wiki/Kin_selection" title="Kin selection">kin selection</a>. Altruists discriminate between the individuals they help and favor relatives. <a href="/wiki/Kin_selection#Hamilton's_rule" title="Kin selection">Hamilton's rule</a> explains the evolutionary rationale behind this selection with the equation <span class="texhtml">c < b × r</span>, where the cost <style data-mw-deduplicate="TemplateStyles:r1003227249">.mw-parser-output .var-serif{font-family:"Nimbus Roman No9 L","Times New Roman",Times,serif;font-size:118%;line-height:1}</style><var class="var-serif">c</var> to the altruist must be less than the benefit <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1003227249"><var class="var-serif">b</var> to the recipient multiplied by the coefficient of relatedness <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1003227249"><var class="var-serif">r</var>. The more closely related two organisms are causes the incidences of altruism to increase because they share many of the same alleles. This means that the altruistic individual, by ensuring that the alleles of its close relative are passed on through survival of its offspring, can forgo the option of having offspring itself because the same number of alleles are passed on. For example, helping a sibling (in diploid animals) has a coefficient of <style data-mw-deduplicate="TemplateStyles:r1154941027">.mw-parser-output .frac{white-space:nowrap}.mw-parser-output .frac .num,.mw-parser-output .frac .den{font-size:80%;line-height:0;vertical-align:super}.mw-parser-output .frac .den{vertical-align:sub}.mw-parser-output .sr-only{border:0;clip:rect(0,0,0,0);clip-path:polygon(0px 0px,0px 0px,0px 0px);height:1px;margin:-1px;overflow:hidden;padding:0;position:absolute;width:1px}</style><span class="frac"><span class="num">1</span>⁄<span class="den">2</span></span>, because (on average) an individual shares half of the alleles in its sibling's offspring. Ensuring that enough of a sibling's offspring survive to adulthood precludes the necessity of the altruistic individual producing offspring.<sup id="cite_ref-qudzyh_125-1" class="reference"><a href="#cite_note-qudzyh-125"><span class="cite-bracket">[</span>122<span class="cite-bracket">]</span></a></sup> The coefficient values depend heavily on the scope of the playing field; for example if the choice of whom to favor includes all genetic living things, not just all relatives, we assume the discrepancy between all humans only accounts for approximately 1% of the diversity in the playing field, a coefficient that was <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1154941027"><span class="frac"><span class="num">1</span>⁄<span class="den">2</span></span> in the smaller field becomes 0.995. Similarly if it is considered that information other than that of a genetic nature (e.g. epigenetics, religion, science, etc.) persisted through time the playing field becomes larger still, and the discrepancies smaller. </p> <div class="mw-heading mw-heading3"><h3 id="Computer_science_and_logic">Computer science and logic</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Game_theory&action=edit&section=34" title="Edit section: Computer science and logic"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Game theory has come to play an increasingly important role in <a href="/wiki/Logic" title="Logic">logic</a> and in <a href="/wiki/Computer_science" title="Computer science">computer science</a>. Several logical theories have a basis in <a href="/wiki/Game_semantics" title="Game semantics">game semantics</a>. In addition, computer scientists have used games to model <a href="/wiki/Interactive_computation" title="Interactive computation">interactive computations</a>. Also, game theory provides a theoretical basis to the field of <a href="/wiki/Multi-agent_system" title="Multi-agent system">multi-agent systems</a>.<sup id="cite_ref-ShohamLeyton-Brown2008_126-0" class="reference"><a href="#cite_note-ShohamLeyton-Brown2008-126"><span class="cite-bracket">[</span>123<span class="cite-bracket">]</span></a></sup> </p><p>Separately, game theory has played a role in <a href="/wiki/Online_algorithm" title="Online algorithm">online algorithms</a>; in particular, the <a href="/wiki/K-server_problem" title="K-server problem"><var style="padding-right: 1px;">k</var>-server problem</a>, which has in the past been referred to as <i>games with moving costs</i> and <i>request-answer games</i>.<sup id="cite_ref-FOOTNOTEBen-DavidBorodinKarpTardos1994_127-0" class="reference"><a href="#cite_note-FOOTNOTEBen-DavidBorodinKarpTardos1994-127"><span class="cite-bracket">[</span>124<span class="cite-bracket">]</span></a></sup> <a href="/wiki/Yao%27s_principle" title="Yao's principle">Yao's principle</a> is a game-theoretic technique for proving <a href="/wiki/Upper_and_lower_bounds" title="Upper and lower bounds">lower bounds</a> on the <a href="/wiki/Analysis_of_algorithms" title="Analysis of algorithms">computational complexity</a> of <a href="/wiki/Randomized_algorithm" title="Randomized algorithm">randomized algorithms</a>, especially online algorithms. </p><p>The emergence of the Internet has motivated the development of algorithms for finding equilibria in games, markets, computational auctions, peer-to-peer systems, and security and information markets. <a href="/wiki/Algorithmic_game_theory" title="Algorithmic game theory">Algorithmic game theory</a><sup id="cite_ref-nisan2007_88-1" class="reference"><a href="#cite_note-nisan2007-88"><span class="cite-bracket">[</span>85<span class="cite-bracket">]</span></a></sup> and within it <a href="/wiki/Algorithmic_mechanism_design" title="Algorithmic mechanism design">algorithmic mechanism design</a><sup id="cite_ref-nisanronen2001_87-1" class="reference"><a href="#cite_note-nisanronen2001-87"><span class="cite-bracket">[</span>84<span class="cite-bracket">]</span></a></sup> combine computational <a href="/wiki/Algorithm_design" class="mw-redirect" title="Algorithm design">algorithm design</a> and analysis of <a href="/wiki/Complex_system" title="Complex system">complex systems</a> with economic theory.<sup id="cite_ref-128" class="reference"><a href="#cite_note-128"><span class="cite-bracket">[</span>125<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-129" class="reference"><a href="#cite_note-129"><span class="cite-bracket">[</span>126<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-130" class="reference"><a href="#cite_note-130"><span class="cite-bracket">[</span>127<span class="cite-bracket">]</span></a></sup> </p><p>Game theory has multiple applications in the field of artificial intelligence and machine learning. It is often used in developing autonomous systems that can make complex decisions in uncertain environment.<sup id="cite_ref-131" class="reference"><a href="#cite_note-131"><span class="cite-bracket">[</span>128<span class="cite-bracket">]</span></a></sup> Some other areas of application of game theory in AI/ML context are as follows - multi-agent system formation, reinforcement learning,<sup id="cite_ref-132" class="reference"><a href="#cite_note-132"><span class="cite-bracket">[</span>129<span class="cite-bracket">]</span></a></sup> mechanism design etc.<sup id="cite_ref-133" class="reference"><a href="#cite_note-133"><span class="cite-bracket">[</span>130<span class="cite-bracket">]</span></a></sup> By using game theory to model the behavior of other agents and anticipate their actions, AI/ML systems can make better decisions and operate more effectively.<sup id="cite_ref-134" class="reference"><a href="#cite_note-134"><span class="cite-bracket">[</span>131<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Philosophy">Philosophy</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Game_theory&action=edit&section=35" title="Edit section: Philosophy"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <table id="Payoff_matrix" style="background:white; float: right; clear:right; text-align:center;" align="right" cellspacing="0" cellpadding="8" width="225"> <tbody><tr> <td style="width:33%;"> </td> <td style="width:33%; border-bottom: solid black 1px;">Stag </td> <td style="width:33%; border-bottom: solid black 1px;">Hare </td></tr> <tr> <td style="border-right: solid black 1px; text-align: right;">Stag </td> <td style="border-right: solid black 1px; border-bottom: solid black 1px; background:white; font-size:120%; white-space:nowrap;">3, 3 </td> <td style="border-right: solid black 1px; border-bottom: solid black 1px; background:white; font-size:120%; white-space:nowrap;">0, 2 </td></tr> <tr> <td style="border-right: solid black 1px; text-align: right;">Hare </td> <td style="border-right: solid black 1px; border-bottom: solid black 1px; background:white; font-size:120%; white-space:nowrap;">2, 0 </td> <td style="border-right: solid black 1px; border-bottom: solid black 1px; background:white; font-size:120%; white-space:nowrap;">2, 2 </td></tr> <tr> <td style="font-size: 90%;" colspan="3"><i>Stag hunt</i> </td></tr></tbody></table> <p>Game theory has been put to several uses in <a href="/wiki/Philosophy" title="Philosophy">philosophy</a>. Responding to two papers by <a href="/wiki/Willard_Van_Orman_Quine" title="Willard Van Orman Quine">W.V.O. Quine</a> (<a href="#CITEREFQuine1960">1960</a>, <a href="#CITEREFQuine1967">1967</a>), <a href="#CITEREFLewis1969">Lewis (1969)</a> used game theory to develop a philosophical account of <a href="/wiki/Convention_(norm)" title="Convention (norm)">convention</a>. In so doing, he provided the first analysis of <a href="/wiki/Common_knowledge_(logic)" title="Common knowledge (logic)">common knowledge</a> and employed it in analyzing play in <a href="/wiki/Coordination_game" title="Coordination game">coordination games</a>. In addition, he first suggested that one can understand <a href="/wiki/Meaning_(semiotics)" title="Meaning (semiotics)">meaning</a> in terms of <a href="/wiki/Signaling_games" class="mw-redirect" title="Signaling games">signaling games</a>. This later suggestion has been pursued by several philosophers since Lewis.<sup id="cite_ref-135" class="reference"><a href="#cite_note-135"><span class="cite-bracket">[</span>132<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-FOOTNOTEGrimKokalisAlai-TaftiKilb2004_136-0" class="reference"><a href="#cite_note-FOOTNOTEGrimKokalisAlai-TaftiKilb2004-136"><span class="cite-bracket">[</span>133<span class="cite-bracket">]</span></a></sup> Following <a href="#CITEREFLewis1969">Lewis (1969)</a> game-theoretic account of conventions, Edna Ullmann-Margalit (1977) and <a href="/wiki/Cristina_Bicchieri" title="Cristina Bicchieri">Bicchieri</a> (2006) have developed theories of <a href="/wiki/Social_norms" class="mw-redirect" title="Social norms">social norms</a> that define them as Nash equilibria that result from transforming a mixed-motive game into a coordination game.<sup id="cite_ref-137" class="reference"><a href="#cite_note-137"><span class="cite-bracket">[</span>134<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-138" class="reference"><a href="#cite_note-138"><span class="cite-bracket">[</span>135<span class="cite-bracket">]</span></a></sup> </p><p>Game theory has also challenged philosophers to think in terms of interactive <a href="/wiki/Epistemology" title="Epistemology">epistemology</a>: what it means for a collective to have common beliefs or knowledge, and what are the consequences of this knowledge for the social outcomes resulting from the interactions of agents. Philosophers who have worked in this area include Bicchieri (1989, 1993),<sup id="cite_ref-139" class="reference"><a href="#cite_note-139"><span class="cite-bracket">[</span>136<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-140" class="reference"><a href="#cite_note-140"><span class="cite-bracket">[</span>137<span class="cite-bracket">]</span></a></sup> <a href="/wiki/Brian_Skyrms" title="Brian Skyrms">Skyrms</a> (1990),<sup id="cite_ref-141" class="reference"><a href="#cite_note-141"><span class="cite-bracket">[</span>138<span class="cite-bracket">]</span></a></sup> and <a href="/wiki/Robert_Stalnaker" title="Robert Stalnaker">Stalnaker</a> (1999).<sup id="cite_ref-142" class="reference"><a href="#cite_note-142"><span class="cite-bracket">[</span>139<span class="cite-bracket">]</span></a></sup> </p><p>The synthesis of game theory with <a href="/wiki/Ethics" title="Ethics">ethics</a> was championed by <a href="/wiki/R._B._Braithwaite" title="R. B. Braithwaite">R. B. Braithwaite</a>.<sup id="cite_ref-143" class="reference"><a href="#cite_note-143"><span class="cite-bracket">[</span>140<span class="cite-bracket">]</span></a></sup> The hope was that rigorous mathematical analysis of game theory might help formalize the more imprecise philosophical discussions. However, this expectation was only materialized to a limited extent.<sup id="cite_ref-144" class="reference"><a href="#cite_note-144"><span class="cite-bracket">[</span>141<span class="cite-bracket">]</span></a></sup> </p><p>In <a href="/wiki/Ethics" title="Ethics">ethics</a>, some (most notably David Gauthier, Gregory Kavka, and Jean Hampton) <sup class="noprint Inline-Template" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Manual_of_Style/Words_to_watch#Unsupported_attributions" title="Wikipedia:Manual of Style/Words to watch"><span title="The material near this tag possibly uses too-vague attribution or weasel words. (July 2012)">who?</span></a></i>]</sup> authors have attempted to pursue <a href="/wiki/Thomas_Hobbes" title="Thomas Hobbes">Thomas Hobbes</a>' project of deriving morality from self-interest. Since games like the <a href="/wiki/Prisoner%27s_dilemma" title="Prisoner's dilemma">prisoner's dilemma</a> present an apparent conflict between morality and self-interest, explaining why cooperation is required by self-interest is an important component of this project. This general strategy is a component of the general <a href="/wiki/Social_contract" title="Social contract">social contract</a> view in <a href="/wiki/Political_philosophy" title="Political philosophy">political philosophy</a> (for examples, see <a href="#CITEREFGauthier1986">Gauthier (1986)</a> and <a href="#CITEREFKavka1986">Kavka (1986)</a>).<sup id="cite_ref-145" class="reference"><a href="#cite_note-145"><span class="cite-bracket">[</span>d<span class="cite-bracket">]</span></a></sup> </p><p>Other authors have attempted to use evolutionary game theory in order to explain the emergence of human attitudes about morality and corresponding animal behaviors. These authors look at several games including the prisoner's dilemma, <a href="/wiki/Stag_hunt" title="Stag hunt">stag hunt</a>, and the <a href="/wiki/Nash_bargaining_game" class="mw-redirect" title="Nash bargaining game">Nash bargaining game</a> as providing an explanation for the emergence of attitudes about morality (see, e.g., Skyrms (<a href="#CITEREFSkyrms1996">1996</a>, <a href="#CITEREFSkyrms2004">2004</a>) and Sober and Wilson (<a href="#CITEREFSoberWilson1998">1998</a>)). </p> <div class="mw-heading mw-heading3"><h3 id="Epidemiology">Epidemiology</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Game_theory&action=edit&section=36" title="Edit section: Epidemiology"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Since the decision to take a vaccine for a particular disease is often made by individuals, who may consider a range of factors and parameters in making this decision (such as the incidence and prevalence of the disease, perceived and real risks associated with contracting the disease, mortality rate, perceived and real risks associated with vaccination, and financial cost of vaccination), game theory has been used to model and predict vaccination uptake in a society.<sup id="cite_ref-146" class="reference"><a href="#cite_note-146"><span class="cite-bracket">[</span>142<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-147" class="reference"><a href="#cite_note-147"><span class="cite-bracket">[</span>143<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Well_known_examples_of_games">Well known examples of games</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Game_theory&action=edit&section=37" title="Edit section: Well known examples of games"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="Prisoner's_dilemma"><span id="Prisoner.27s_dilemma"></span>Prisoner's dilemma</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Game_theory&action=edit&section=38" title="Edit section: Prisoner's dilemma"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Prisoner%27s_dilemma" title="Prisoner's dilemma">Prisoner's dilemma</a></div> <table class="wikitable floatright"> <caption>Standard prisoner's dilemma payoff matrix </caption> <tbody><tr> <th style="background:#EAECF0;background:linear-gradient(to top right,#EAECF0 49%,#AAA 49.5%,#AAA 50.5%,#EAECF0 51%);line-height:1.2;padding:0.1em 0.4em;"><div style="margin-left:2em;text-align:right">B</div><div style="margin-right:2em;text-align:left">A</div> </th> <th>B stays<br />silent </th> <th>B<br />betrays </th></tr> <tr> <th>A stays<br />silent </th> <td style="background:transparent;background:linear-gradient(to top right,transparent 49%,#AAA 49.5%,#AAA 50.5%,transparent 51%);line-height:1.2;padding:0.1em 0.4em;"><div style="margin-left:2em;text-align:right">−2</div><div style="margin-right:2em;text-align:left">−2</div> </td> <td style="background:transparent;background:linear-gradient(to top right,transparent 49%,#AAA 49.5%,#AAA 50.5%,transparent 51%);line-height:1.2;padding:0.1em 0.4em;"><div style="margin-left:2em;text-align:right">0</div><div style="margin-right:2em;text-align:left">−10</div> </td></tr> <tr> <th>A<br />betrays </th> <td style="background:transparent;background:linear-gradient(to top right,transparent 49%,#AAA 49.5%,#AAA 50.5%,transparent 51%);line-height:1.2;padding:0.1em 0.4em;"><div style="margin-left:2em;text-align:right">−10</div><div style="margin-right:2em;text-align:left">0</div> </td> <td style="background:transparent;background:linear-gradient(to top right,transparent 49%,#AAA 49.5%,#AAA 50.5%,transparent 51%);line-height:1.2;padding:0.1em 0.4em;"><div style="margin-left:2em;text-align:right">−5</div><div style="margin-right:2em;text-align:left">−5</div> </td></tr></tbody></table> <p><a href="/wiki/William_Poundstone" title="William Poundstone">William Poundstone</a> described the game in his 1993 book Prisoner's Dilemma:<sup id="cite_ref-FOOTNOTEPoundstone19938,_117_148-0" class="reference"><a href="#cite_note-FOOTNOTEPoundstone19938,_117-148"><span class="cite-bracket">[</span>144<span class="cite-bracket">]</span></a></sup> </p><p>Two members of a criminal gang, A and B, are arrested and imprisoned. Each prisoner is in solitary confinement with no means of communication with their partner. The principal charge would lead to a sentence of ten years in prison; however, the police do not have the evidence for a conviction. They plan to sentence both to two years in prison on a lesser charge but offer each prisoner a Faustian bargain: If one of them confesses to the crime of the principal charge, betraying the other, they will be pardoned and free to leave while the other must serve the entirety of the sentence instead of just two years for the lesser charge. </p><p>The <a href="/wiki/Dominant_strategy" class="mw-redirect" title="Dominant strategy">dominant strategy</a> (and therefore the best response to any possible opponent strategy), is to betray the other, which aligns with the <a href="/wiki/Sure-thing_principle" title="Sure-thing principle">sure-thing principle</a>.<sup id="cite_ref-149" class="reference"><a href="#cite_note-149"><span class="cite-bracket">[</span>145<span class="cite-bracket">]</span></a></sup> However, both prisoners staying silent would yield a greater reward for both of them than mutual betrayal. </p> <div class="mw-heading mw-heading3"><h3 id="Battle_of_the_sexes">Battle of the sexes</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Game_theory&action=edit&section=39" title="Edit section: Battle of the sexes"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Battle_of_the_sexes_(game_theory)" title="Battle of the sexes (game theory)">Battle of the sexes (game theory)</a></div> <p>The "battle of the sexes" is a term used to describe the perceived conflict between men and women in various areas of life, such as relationships, careers, and social roles. This conflict is often portrayed in popular culture, such as movies and television shows, as a humorous or dramatic competition between the genders. This conflict can be depicted in a game theory framework. This is an example of non-cooperative games. </p><p>An example of the "battle of the sexes" can be seen in the portrayal of relationships in popular media, where men and women are often depicted as being fundamentally different and in conflict with each other. For instance, in some romantic comedies, the male and female protagonists are shown as having opposing views on love and relationships, and they have to overcome these differences in order to be together.<sup id="cite_ref-150" class="reference"><a href="#cite_note-150"><span class="cite-bracket">[</span>146<span class="cite-bracket">]</span></a></sup> </p><p>In this game, there are two pure strategy Nash equilibria: one where both the players choose the same strategy and the other where the players choose different options. If the game is played in mixed strategies, where each player chooses their strategy randomly, then there is an infinite number of Nash equilibria. However, in the context of the "battle of the sexes" game, the assumption is usually made that the game is played in pure strategies.<sup id="cite_ref-151" class="reference"><a href="#cite_note-151"><span class="cite-bracket">[</span>147<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Ultimatum_game">Ultimatum game</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Game_theory&action=edit&section=40" title="Edit section: Ultimatum game"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Ultimatum_game" title="Ultimatum game">Ultimatum game</a></div> <p>The ultimatum game is a game that has become a popular instrument of <a href="/wiki/Experimental_economics" title="Experimental economics">economic experiments</a>. An early description is by Nobel laureate <a href="/wiki/John_Harsanyi" title="John Harsanyi">John Harsanyi</a> in 1961.<sup id="cite_ref-152" class="reference"><a href="#cite_note-152"><span class="cite-bracket">[</span>148<span class="cite-bracket">]</span></a></sup> </p><p>One player, the proposer, is endowed with a sum of money. The proposer is tasked with splitting it with another player, the responder (who knows what the total sum is). Once the proposer communicates his decision, the responder may accept it or reject it. If the responder accepts, the money is split per the proposal; if the responder rejects, both players receive nothing. Both players know in advance the consequences of the responder accepting or rejecting the offer. The game demonstrates how social acceptance, fairness, and generosity influence the players decisions.<sup id="cite_ref-153" class="reference"><a href="#cite_note-153"><span class="cite-bracket">[</span>149<span class="cite-bracket">]</span></a></sup> </p><p>Ultimatum game has a variant, that is the dictator game. They are mostly identical, except in dictator game the responder has no power to reject the proposer's offer. </p> <div class="mw-heading mw-heading3"><h3 id="Trust_game">Trust game</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Game_theory&action=edit&section=41" title="Edit section: Trust game"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The Trust Game is an experiment designed to measure trust in economic decisions. It is also called "the investment game" and is designed to investigate trust and demonstrate its importance rather than "rationality" of self-interest. The game was designed by Berg Joyce, John Dickhaut and Kevin McCabe in 1995.<sup id="cite_ref-154" class="reference"><a href="#cite_note-154"><span class="cite-bracket">[</span>150<span class="cite-bracket">]</span></a></sup> </p><p>In the game, one player (the investor) is given a sum of money and must decide how much of it to give to another player (the trustee). The amount given is then tripled by the experimenter. The trustee then decides how much of the tripled amount to return to the investor. If the recipient is completely self interested, then he/she should return nothing. However that is not true as the experiment conduct. The outcome suggest that people are willing to place a trust, by risking some amount of money, in the belief that there would be reciprocity.<sup id="cite_ref-155" class="reference"><a href="#cite_note-155"><span class="cite-bracket">[</span>151<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Cournot_Competition">Cournot Competition</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Game_theory&action=edit&section=42" title="Edit section: Cournot Competition"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Cournot_competition" title="Cournot competition">Cournot competition</a></div> <p>The Cournot competition model involves players choosing quantity of a homogenous product to produce independently and simultaneously, where <a href="/wiki/Marginal_cost" title="Marginal cost">marginal cost</a> can be different for each firm and the firm's payoff is profit. The production costs are public information and the firm aims to find their profit-maximizing quantity based on what they believe the other firm will produce and behave like monopolies. In this game firms want to produce at the monopoly quantity but there is a high incentive to deviate and produce more, which decreases the market-clearing price.<sup id="cite_ref-:2_23-1" class="reference"><a href="#cite_note-:2-23"><span class="cite-bracket">[</span>22<span class="cite-bracket">]</span></a></sup> For example, firms may be tempted to deviate from the monopoly quantity if there is a low monopoly quantity and high price, with the aim of increasing production to maximize profit.<sup id="cite_ref-:2_23-2" class="reference"><a href="#cite_note-:2-23"><span class="cite-bracket">[</span>22<span class="cite-bracket">]</span></a></sup> However this option does not provide the highest payoff, as a firm's ability to maximize profits depends on its market share and the elasticity of the market demand.<sup id="cite_ref-156" class="reference"><a href="#cite_note-156"><span class="cite-bracket">[</span>152<span class="cite-bracket">]</span></a></sup> The Cournot equilibrium is reached when each firm operates on their reaction function with no incentive to deviate, as they have the best response based on the other firms output.<sup id="cite_ref-:2_23-3" class="reference"><a href="#cite_note-:2-23"><span class="cite-bracket">[</span>22<span class="cite-bracket">]</span></a></sup> Within the game, firms reach the Nash equilibrium when the Cournot equilibrium is achieved. </p> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Cournot_Duopoly_Nash_equilibrium.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/7/7d/Cournot_Duopoly_Nash_equilibrium.png/220px-Cournot_Duopoly_Nash_equilibrium.png" decoding="async" width="220" height="174" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/7/7d/Cournot_Duopoly_Nash_equilibrium.png/330px-Cournot_Duopoly_Nash_equilibrium.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/7/7d/Cournot_Duopoly_Nash_equilibrium.png/440px-Cournot_Duopoly_Nash_equilibrium.png 2x" data-file-width="672" data-file-height="530" /></a><figcaption>Equilibrium for Cournot quantity competition</figcaption></figure> <div class="mw-heading mw-heading3"><h3 id="Bertrand_Competition">Bertrand Competition</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Game_theory&action=edit&section=43" title="Edit section: Bertrand Competition"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Bertrand_competition" title="Bertrand competition">Bertrand competition</a></div> <p>The Bertrand competition assumes homogenous products and a constant marginal cost and players choose the prices.<sup id="cite_ref-:2_23-4" class="reference"><a href="#cite_note-:2-23"><span class="cite-bracket">[</span>22<span class="cite-bracket">]</span></a></sup> The equilibrium of price competition is where the price is equal to marginal costs, assuming complete information about the competitors' costs. Therefore, the firms have an incentive to deviate from the equilibrium because a homogenous product with a lower price will gain all of the market share, known as a cost advantage.<sup id="cite_ref-157" class="reference"><a href="#cite_note-157"><span class="cite-bracket">[</span>153<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="In_popular_culture">In popular culture</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Game_theory&action=edit&section=44" title="Edit section: In popular culture"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li>Based on <a href="/wiki/A_Beautiful_Mind_(book)" title="A Beautiful Mind (book)">the 1998 book</a> by <a href="/wiki/Sylvia_Nasar" title="Sylvia Nasar">Sylvia Nasar</a>,<sup id="cite_ref-158" class="reference"><a href="#cite_note-158"><span class="cite-bracket">[</span>154<span class="cite-bracket">]</span></a></sup> the life story of game theorist and mathematician <a href="/wiki/John_Forbes_Nash_Jr." title="John Forbes Nash Jr.">John Nash</a> was turned into the 2001 <a href="/wiki/Biopic" class="mw-redirect" title="Biopic">biopic</a> <i><a href="/wiki/A_Beautiful_Mind_(film)" title="A Beautiful Mind (film)">A Beautiful Mind</a></i>, starring <a href="/wiki/Russell_Crowe" title="Russell Crowe">Russell Crowe</a> as Nash.<sup id="cite_ref-159" class="reference"><a href="#cite_note-159"><span class="cite-bracket">[</span>155<span class="cite-bracket">]</span></a></sup></li> <li>The 1959 <a href="/wiki/Military_science_fiction" title="Military science fiction">military science fiction</a> novel <i><a href="/wiki/Starship_Troopers" title="Starship Troopers">Starship Troopers</a></i> by <a href="/wiki/Robert_A._Heinlein" title="Robert A. Heinlein">Robert A. Heinlein</a> mentioned "games theory" and "theory of games".<sup id="cite_ref-160" class="reference"><a href="#cite_note-160"><span class="cite-bracket">[</span>156<span class="cite-bracket">]</span></a></sup> In the 1997 film <a href="/wiki/Starship_Troopers_(film)" title="Starship Troopers (film)">of the same name</a>, the character Carl Jenkins referred to his military intelligence assignment as being assigned to "games and theory".</li> <li>The 1964 film <i><a href="/wiki/Dr._Strangelove" title="Dr. Strangelove">Dr. Strangelove</a></i> satirizes game theoretic ideas about <a href="/wiki/Deterrence_theory" title="Deterrence theory">deterrence theory</a>. For example, nuclear deterrence depends on the threat to retaliate catastrophically if a nuclear attack is detected. A game theorist might argue that such threats can fail to be <i>credible</i>, in the sense that they can lead to subgame imperfect equilibria. The movie takes this idea one step further, with the Soviet Union irrevocably committing to a catastrophic nuclear response without making the threat public.<sup id="cite_ref-161" class="reference"><a href="#cite_note-161"><span class="cite-bracket">[</span>157<span class="cite-bracket">]</span></a></sup></li> <li>The 1980s <a href="/wiki/Power_pop" title="Power pop">power pop</a> band <a href="/wiki/Game_Theory_(band)" title="Game Theory (band)">Game Theory</a> was founded by singer/songwriter <a href="/wiki/Scott_Miller_(pop_musician)" title="Scott Miller (pop musician)">Scott Miller</a>, who described the band's name as alluding to "the study of calculating the most appropriate action given an adversary<span class="nowrap"> </span>... to give yourself the minimum amount of failure".<sup id="cite_ref-intpacsun_162-0" class="reference"><a href="#cite_note-intpacsun-162"><span class="cite-bracket">[</span>158<span class="cite-bracket">]</span></a></sup></li> <li><i><a href="/wiki/Liar_Game" title="Liar Game">Liar Game</a></i>, a 2005 Japanese <a href="/wiki/Manga" title="Manga">manga</a> and 2007 television series, presents the main characters in each episode with a game or problem that is typically drawn from game theory, as demonstrated by the strategies applied by the characters.<sup id="cite_ref-163" class="reference"><a href="#cite_note-163"><span class="cite-bracket">[</span>159<span class="cite-bracket">]</span></a></sup></li> <li>The 1974 novel <i><a href="/wiki/Spy_Story_(novel)" title="Spy Story (novel)">Spy Story</a></i> by <a href="/wiki/Len_Deighton" title="Len Deighton">Len Deighton</a> explores elements of game theory in regard to cold war army exercises.</li> <li>The 2008 novel <i><a href="/wiki/The_Dark_Forest" title="The Dark Forest">The Dark Forest</a></i> by <a href="/wiki/Liu_Cixin" title="Liu Cixin">Liu Cixin</a> explores the relationship between extraterrestrial life, humanity, and game theory.</li> <li>Joker, the prime antagonist in the 2008 film <i><a href="/wiki/The_Dark_Knight" title="The Dark Knight">The Dark Knight</a></i> presents game theory concepts—notably the <a href="/wiki/Prisoner%27s_dilemma" title="Prisoner's dilemma">prisoner's dilemma</a> in a scene where he asks passengers in two different ferries to bomb the other one to save their own.</li> <li>In the 2018 film <i><a href="/wiki/Crazy_Rich_Asians_(film)" title="Crazy Rich Asians (film)">Crazy Rich Asians</a></i>, the female lead Rachel Chu is a professor of economics and game theory at <a href="/wiki/New_York_University" title="New York University">New York University</a>. At the beginning of the film she is seen in her NYU classroom playing a game of poker with her teaching assistant and wins the game by <a href="/wiki/Glossary_of_card_game_terms#bluffing" title="Glossary of card game terms">bluffing</a>;<sup id="cite_ref-164" class="reference"><a href="#cite_note-164"><span class="cite-bracket">[</span>160<span class="cite-bracket">]</span></a></sup> then in the <a href="/wiki/Climax_(narrative)" title="Climax (narrative)">climax</a> of the film, she plays a game of <a href="/wiki/Mahjong" title="Mahjong">mahjong</a> with her boyfriend's disapproving mother Eleanor, losing the game to Eleanor on purpose but winning her approval as a result.<sup id="cite_ref-165" class="reference"><a href="#cite_note-165"><span class="cite-bracket">[</span>161<span class="cite-bracket">]</span></a></sup></li> <li>In the 2017 film <a href="/wiki/Molly%27s_Game" title="Molly's Game">Molly's Game</a>, Brad, an inexperienced poker player, makes an irrational betting decision without realizing and causes his opponent Harlan to deviate from his Nash Equilibrium strategy, resulting in a significant loss when Harlan loses the hand.<sup id="cite_ref-166" class="reference"><a href="#cite_note-166"><span class="cite-bracket">[</span>162<span class="cite-bracket">]</span></a></sup></li></ul> <div class="mw-heading mw-heading2"><h2 id="See_also">See also</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Game_theory&action=edit&section=45" title="Edit section: See also"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/Applied_ethics" title="Applied ethics">Applied ethics</a> – Practical application of moral considerations</li> <li><a href="/wiki/Bandwidth-sharing_game" title="Bandwidth-sharing game">Bandwidth-sharing game</a> – Type of resource allocation game</li> <li><a href="/wiki/Chainstore_paradox" title="Chainstore paradox">Chainstore paradox</a> – Game theory paradox</li> <li><a href="/wiki/Collective_intentionality" title="Collective intentionality">Collective intentionality</a> – Intentionality that occurs when two or more individuals undertake a task together</li> <li><a href="/wiki/Core_(game_theory)" title="Core (game theory)">Core (game theory)</a> – term in game theory<span style="display:none" class="category-wikidata-fallback-annotation">Pages displaying wikidata descriptions as a fallback</span></li> <li><a href="/wiki/Glossary_of_game_theory" title="Glossary of game theory">Glossary of game theory</a></li> <li><a href="/wiki/Intra-household_bargaining" title="Intra-household bargaining">Intra-household bargaining</a> – negotiations between members of a household to reach decisions<span style="display:none" class="category-wikidata-fallback-annotation">Pages displaying wikidata descriptions as a fallback</span></li> <li><a href="/wiki/Kingmaker_scenario" title="Kingmaker scenario">Kingmaker scenario</a> – an endgame situation where a player who is unable to win has the capacity to determine which player among others will win<span style="display:none" class="category-wikidata-fallback-annotation">Pages displaying wikidata descriptions as a fallback</span></li> <li><a href="/wiki/Law_and_economics" title="Law and economics">Law and economics</a> – Application of economic theory to analysis of legal systems</li> <li><a href="/wiki/Mutual_assured_destruction" title="Mutual assured destruction">Mutual assured destruction</a> – Doctrine of military strategy</li> <li><a href="/wiki/Outline_of_artificial_intelligence" title="Outline of artificial intelligence">Outline of artificial intelligence</a> – Overview of and topical guide to artificial intelligence</li> <li><a href="/wiki/Parrondo%27s_paradox" title="Parrondo's paradox">Parrondo's paradox</a> – Paradox in game theory</li> <li><a href="/wiki/Precautionary_principle" title="Precautionary principle">Precautionary principle</a> – Risk management strategy</li> <li><a href="/wiki/Quantum_refereed_game" title="Quantum refereed game">Quantum refereed game</a></li> <li><a href="/wiki/Risk_management" title="Risk management">Risk management</a> – Identification, evaluation and control of risks</li> <li><a href="/wiki/Self-confirming_equilibrium" title="Self-confirming equilibrium">Self-confirming equilibrium</a></li> <li><a href="/wiki/Tragedy_of_the_commons" title="Tragedy of the commons">Tragedy of the commons</a> – Self-interests causing depletion of a shared resource</li> <li><a href="/wiki/Traveler%27s_dilemma" title="Traveler's dilemma">Traveler's dilemma</a> – non-zero-sum game thought experiment<span style="display:none" class="category-wikidata-fallback-annotation">Pages displaying wikidata descriptions as a fallback</span></li> <li><a href="/wiki/Wilson_doctrine_(economics)" title="Wilson doctrine (economics)">Wilson doctrine (economics)</a> – Argument in economic theory</li> <li><a href="/wiki/Compositional_game_theory" title="Compositional game theory">Compositional game theory</a></li></ul> <p><b>Lists</b> </p> <ul><li><a href="/wiki/List_of_cognitive_biases" title="List of cognitive biases">List of cognitive biases</a></li> <li><a href="/wiki/List_of_emerging_technologies" title="List of emerging technologies">List of emerging technologies</a></li> <li><a href="/wiki/List_of_games_in_game_theory" title="List of games in game theory">List of games in game theory</a></li></ul> <div class="mw-heading mw-heading2"><h2 id="Notes">Notes</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Game_theory&action=edit&section=46" title="Edit section: Notes"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1239543626">.mw-parser-output .reflist{margin-bottom:0.5em;list-style-type:decimal}@media screen{.mw-parser-output .reflist{font-size:90%}}.mw-parser-output .reflist .references{font-size:100%;margin-bottom:0;list-style-type:inherit}.mw-parser-output .reflist-columns-2{column-width:30em}.mw-parser-output .reflist-columns-3{column-width:25em}.mw-parser-output .reflist-columns{margin-top:0.3em}.mw-parser-output .reflist-columns ol{margin-top:0}.mw-parser-output .reflist-columns li{page-break-inside:avoid;break-inside:avoid-column}.mw-parser-output .reflist-upper-alpha{list-style-type:upper-alpha}.mw-parser-output .reflist-upper-roman{list-style-type:upper-roman}.mw-parser-output .reflist-lower-alpha{list-style-type:lower-alpha}.mw-parser-output .reflist-lower-greek{list-style-type:lower-greek}.mw-parser-output .reflist-lower-roman{list-style-type:lower-roman}</style><div class="reflist reflist-lower-alpha"> <div class="mw-references-wrap"><ol class="references"> <li id="cite_note-16"><span class="mw-cite-backlink"><b><a href="#cite_ref-16">^</a></b></span> <span class="reference-text">Although common knowledge was first discussed by the philosopher <a href="/wiki/David_Kellogg_Lewis" class="mw-redirect" title="David Kellogg Lewis">David Lewis</a> in his dissertation (and later book) <i>Convention</i> in the late 1960s, it was not widely considered by economists until <a href="/wiki/Robert_Aumann" title="Robert Aumann">Robert Aumann</a>'s work in the 1970s.</span> </li> <li id="cite_note-75"><span class="mw-cite-backlink"><b><a href="#cite_ref-75">^</a></b></span> <span class="reference-text">Experimental work in game theory goes by many names, <a href="/wiki/Experimental_economics" title="Experimental economics">experimental economics</a>, <a href="/wiki/Behavioral_economics" title="Behavioral economics">behavioral economics</a>, and <a href="/wiki/Behavioural_game_theory" class="mw-redirect" title="Behavioural game theory">behavioural game theory</a> are several.<sup id="cite_ref-74" class="reference"><a href="#cite_note-74"><span class="cite-bracket">[</span>73<span class="cite-bracket">]</span></a></sup></span> </li> <li id="cite_note-77"><span class="mw-cite-backlink"><b><a href="#cite_ref-77">^</a></b></span> <span class="reference-text">At <a href="/wiki/JEL_classification_codes#Mathematical_and_quantitative_methods_JEL:_C_Subcategories" title="JEL classification codes">JEL:C7</a> of the <i><a href="/wiki/Journal_of_Economic_Literature" title="Journal of Economic Literature">Journal of Economic Literature</a></i> classification codes.</span> </li> <li id="cite_note-145"><span class="mw-cite-backlink"><b><a href="#cite_ref-145">^</a></b></span> <span class="reference-text">For a more detailed discussion of the use of game theory in ethics, see the Stanford Encyclopedia of Philosophy's entry <a rel="nofollow" class="external text" href="http://plato.stanford.edu/entries/game-ethics/">game theory and ethics</a>.</span> </li> </ol></div></div> <div class="mw-heading mw-heading2"><h2 id="References">References</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Game_theory&action=edit&section=47" title="Edit section: References"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1239543626"><div class="reflist"> <div class="mw-references-wrap mw-references-columns"><ol class="references"> <li id="cite_note-Myerson-1"><span class="mw-cite-backlink">^ <a href="#cite_ref-Myerson_1-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-Myerson_1-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><style data-mw-deduplicate="TemplateStyles:r1238218222">.mw-parser-output cite.citation{font-style:inherit;word-wrap:break-word}.mw-parser-output .citation q{quotes:"\"""\"""'""'"}.mw-parser-output .citation:target{background-color:rgba(0,127,255,0.133)}.mw-parser-output .id-lock-free.id-lock-free a{background:url("//upload.wikimedia.org/wikipedia/commons/6/65/Lock-green.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-limited.id-lock-limited a,.mw-parser-output .id-lock-registration.id-lock-registration a{background:url("//upload.wikimedia.org/wikipedia/commons/d/d6/Lock-gray-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-subscription.id-lock-subscription a{background:url("//upload.wikimedia.org/wikipedia/commons/a/aa/Lock-red-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .cs1-ws-icon a{background:url("//upload.wikimedia.org/wikipedia/commons/4/4c/Wikisource-logo.svg")right 0.1em center/12px no-repeat}body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-free a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-limited a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-registration a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-subscription a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .cs1-ws-icon a{background-size:contain;padding:0 1em 0 0}.mw-parser-output .cs1-code{color:inherit;background:inherit;border:none;padding:inherit}.mw-parser-output .cs1-hidden-error{display:none;color:var(--color-error,#d33)}.mw-parser-output .cs1-visible-error{color:var(--color-error,#d33)}.mw-parser-output .cs1-maint{display:none;color:#085;margin-left:0.3em}.mw-parser-output .cs1-kern-left{padding-left:0.2em}.mw-parser-output .cs1-kern-right{padding-right:0.2em}.mw-parser-output .citation .mw-selflink{font-weight:inherit}@media screen{.mw-parser-output .cs1-format{font-size:95%}html.skin-theme-clientpref-night .mw-parser-output .cs1-maint{color:#18911f}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .cs1-maint{color:#18911f}}</style><cite id="CITEREFMyerson1991" class="citation book cs1"><a href="/wiki/Roger_B._Myerson" class="mw-redirect" title="Roger B. Myerson">Myerson, Roger B.</a> (1991). <i>Game Theory: Analysis of Conflict</i>. <a href="/wiki/Harvard_University_Press" title="Harvard University Press">Harvard University Press</a>. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/9780674341166" title="Special:BookSources/9780674341166"><bdi>9780674341166</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Game+Theory%3A+Analysis+of+Conflict&rft.pub=Harvard+University+Press&rft.date=1991&rft.isbn=9780674341166&rft.aulast=Myerson&rft.aufirst=Roger+B.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGame+theory" class="Z3988"></span></span> </li> <li id="cite_note-2"><span class="mw-cite-backlink"><b><a href="#cite_ref-2">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFShapleyShubik1971" class="citation book cs1">Shapley, Lloyd S.; Shubik, Martin (1 January 1971). "Chapter 1, Introduction, The Use of Models". <a rel="nofollow" class="external text" href="https://www.rand.org/pubs/reports/R0904z1.html"><i>Game Theory in Economics</i></a>. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20230423130243/https://www.rand.org/pubs/reports/R0904z1.html">Archived</a> from the original on 23 April 2023<span class="reference-accessdate">. Retrieved <span class="nowrap">23 April</span> 2023</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=Chapter+1%2C+Introduction%2C+The+Use+of+Models&rft.btitle=Game+Theory+in+Economics&rft.date=1971-01-01&rft.aulast=Shapley&rft.aufirst=Lloyd+S.&rft.au=Shubik%2C+Martin&rft_id=https%3A%2F%2Fwww.rand.org%2Fpubs%2Freports%2FR0904z1.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGame+theory" class="Z3988"></span></span> </li> <li id="cite_note-3"><span class="mw-cite-backlink"><b><a href="#cite_ref-3">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFNeumannMorgenstern2007" class="citation book cs1">Neumann, John von; Morgenstern, Oskar (8 April 2007). <a rel="nofollow" class="external text" href="https://press.princeton.edu/books/paperback/9780691130613/theory-of-games-and-economic-behavior"><i>Theory of Games and Economic Behavior</i></a>. Princeton University Press. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-691-13061-3" title="Special:BookSources/978-0-691-13061-3"><bdi>978-0-691-13061-3</bdi></a>. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20230328004503/https://press.princeton.edu/books/paperback/9780691130613/theory-of-games-and-economic-behavior">Archived</a> from the original on 28 March 2023<span class="reference-accessdate">. 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In Weintraub, E. Roy (ed.). <i>Toward a History of Game Theory</i>. Durham: Duke University Press. pp. 113–147. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-8223-1253-6" title="Special:BookSources/978-0-8223-1253-6"><bdi>978-0-8223-1253-6</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=What+Were+von+Neumann+and+Morgenstern+Trying+to+Accomplish%3F&rft.btitle=Toward+a+History+of+Game+Theory&rft.place=Durham&rft.pages=113-147&rft.pub=Duke+University+Press&rft.date=1992&rft.isbn=978-0-8223-1253-6&rft.aulast=Mirowski&rft.aufirst=Philip&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3D9CHY2Gozh1MC%26pg%3DPA113&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGame+theory" class="Z3988"></span></span> </li> <li id="cite_note-13"><span class="mw-cite-backlink"><b><a href="#cite_ref-13">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFLeonard2010" class="citation cs2">Leonard, Robert (2010), <i>Von Neumann, Morgenstern, and the Creation of Game Theory</i>, New York: Cambridge University Press, <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1017%2FCBO9780511778278">10.1017/CBO9780511778278</a>, <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-521-56266-9" title="Special:BookSources/978-0-521-56266-9"><bdi>978-0-521-56266-9</bdi></a></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Von+Neumann%2C+Morgenstern%2C+and+the+Creation+of+Game+Theory&rft.place=New+York&rft.pub=Cambridge+University+Press&rft.date=2010&rft_id=info%3Adoi%2F10.1017%2FCBO9780511778278&rft.isbn=978-0-521-56266-9&rft.aulast=Leonard&rft.aufirst=Robert&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGame+theory" class="Z3988"></span></span> </li> <li id="cite_note-14"><span class="mw-cite-backlink"><b><a href="#cite_ref-14">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFKim2014" class="citation book cs1">Kim, Sungwook, ed. 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Retrieved <span class="nowrap">15 September</span> 2016</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=GameTheory.net&rft.atitle=Non-Cooperative+Game&rft.aulast=Shor&rft.aufirst=Mike&rft_id=http%3A%2F%2Fwww.gametheory.net%2Fdictionary%2FNon-CooperativeGame.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGame+theory" class="Z3988"></span></span> </li> <li id="cite_note-18"><span class="mw-cite-backlink"><b><a href="#cite_ref-18">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFChandrasekaran" class="citation web cs1">Chandrasekaran, Ramaswamy. <a rel="nofollow" class="external text" href="http://www.utdallas.edu/~chandra/documents/6311/coopgames.pdf">"Cooperative Game Theory"</a> <span class="cs1-format">(PDF)</span>. University of Texas at Dallas. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20160418101712/http://www.utdallas.edu/~chandra/documents/6311/coopgames.pdf">Archived</a> <span class="cs1-format">(PDF)</span> from the original on 18 April 2016.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Cooperative+Game+Theory&rft.pub=University+of+Texas+at+Dallas&rft.aulast=Chandrasekaran&rft.aufirst=Ramaswamy&rft_id=http%3A%2F%2Fwww.utdallas.edu%2F~chandra%2Fdocuments%2F6311%2Fcoopgames.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGame+theory" class="Z3988"></span></span> </li> <li id="cite_note-19"><span class="mw-cite-backlink"><b><a href="#cite_ref-19">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFBrandenburger" class="citation web cs1">Brandenburger, Adam. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20170829084624/http://www.uib.cat/depart/deeweb/pdi/hdeelbm0/arxius_decisions_and_games/cooperative_game_theory-brandenburger.pdf">"Cooperative Game Theory: Characteristic Functions, Allocations, Marginal Contribution"</a> <span class="cs1-format">(PDF)</span>. Archived from <a rel="nofollow" class="external text" href="http://www.uib.cat/depart/deeweb/pdi/hdeelbm0/arxius_decisions_and_games/cooperative_game_theory-brandenburger.pdf">the original</a> <span class="cs1-format">(PDF)</span> on 29 August 2017<span class="reference-accessdate">. Retrieved <span class="nowrap">14 April</span> 2020</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Cooperative+Game+Theory%3A+Characteristic+Functions%2C+Allocations%2C+Marginal+Contribution&rft.aulast=Brandenburger&rft.aufirst=Adam&rft_id=http%3A%2F%2Fwww.uib.cat%2Fdepart%2Fdeeweb%2Fpdi%2Fhdeelbm0%2Farxius_decisions_and_games%2Fcooperative_game_theory-brandenburger.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGame+theory" class="Z3988"></span></span> </li> <li id="cite_note-20"><span class="mw-cite-backlink"><b><a href="#cite_ref-20">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFShor2006" class="citation web cs1">Shor, Mike (2006). <a rel="nofollow" class="external text" href="https://www.gametheory.net/dictionary/Games/SymmetricGame.html">"Symmetric Game"</a>. <i>Game Theory.net</i>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=Game+Theory.net&rft.atitle=Symmetric+Game&rft.date=2006&rft.aulast=Shor&rft.aufirst=Mike&rft_id=https%3A%2F%2Fwww.gametheory.net%2Fdictionary%2FGames%2FSymmetricGame.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGame+theory" class="Z3988"></span></span> </li> <li id="cite_note-21"><span class="mw-cite-backlink"><b><a href="#cite_ref-21">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFOwen1995" class="citation book cs1"><a href="/wiki/Guillermo_Owen" title="Guillermo Owen">Owen, Guillermo</a> (1995). <i>Game Theory: Third Edition</i>. Bingley: Emerald Group Publishing. p. 11. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-12-531151-9" title="Special:BookSources/978-0-12-531151-9"><bdi>978-0-12-531151-9</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Game+Theory%3A+Third+Edition&rft.place=Bingley&rft.pages=11&rft.pub=Emerald+Group+Publishing&rft.date=1995&rft.isbn=978-0-12-531151-9&rft.aulast=Owen&rft.aufirst=Guillermo&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGame+theory" class="Z3988"></span></span> </li> <li id="cite_note-22"><span class="mw-cite-backlink"><b><a href="#cite_ref-22">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFChang2015" class="citation book cs1">Chang, Kuang-Hua (2015). "Decisions in Engineering Design". <i>Design Theory and Methods Using CAD/CAE</i>. pp. 39–101. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1016%2Fb978-0-12-398512-5.00002-5">10.1016/b978-0-12-398512-5.00002-5</a>. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-12-398512-5" title="Special:BookSources/978-0-12-398512-5"><bdi>978-0-12-398512-5</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=Decisions+in+Engineering+Design&rft.btitle=Design+Theory+and+Methods+Using+CAD%2FCAE&rft.pages=39-101&rft.date=2015&rft_id=info%3Adoi%2F10.1016%2Fb978-0-12-398512-5.00002-5&rft.isbn=978-0-12-398512-5&rft.aulast=Chang&rft.aufirst=Kuang-Hua&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGame+theory" class="Z3988"></span></span> </li> <li id="cite_note-:2-23"><span class="mw-cite-backlink">^ <a href="#cite_ref-:2_23-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-:2_23-1"><sup><i><b>b</b></i></sup></a> <a href="#cite_ref-:2_23-2"><sup><i><b>c</b></i></sup></a> <a href="#cite_ref-:2_23-3"><sup><i><b>d</b></i></sup></a> <a href="#cite_ref-:2_23-4"><sup><i><b>e</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFGibbons1992" class="citation book cs1">Gibbons, Robert (1992). <i>Game Theory for Applied Economists</i>. Princeton, New Jersey: Princeton University Press. pp. 14–17. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-691-04308-6" title="Special:BookSources/0-691-04308-6"><bdi>0-691-04308-6</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Game+Theory+for+Applied+Economists&rft.place=Princeton%2C+New+Jersey&rft.pages=14-17&rft.pub=Princeton+University+Press&rft.date=1992&rft.isbn=0-691-04308-6&rft.aulast=Gibbons&rft.aufirst=Robert&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGame+theory" class="Z3988"></span></span> </li> <li id="cite_note-24"><span class="mw-cite-backlink"><b><a href="#cite_ref-24">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFFerguson" class="citation web cs1"><a href="/wiki/Thomas_S._Ferguson" title="Thomas S. Ferguson">Ferguson, Thomas S.</a> <a rel="nofollow" class="external text" href="https://www.math.ucla.edu/~tom/Game_Theory/mat.pdf#page=56">"Game Theory"</a> <span class="cs1-format">(PDF)</span>. UCLA Department of Mathematics. pp. 56–57. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20040730140255/http://www.math.ucla.edu/~tom/Game_Theory/mat.pdf">Archived</a> <span class="cs1-format">(PDF)</span> from the original on 30 July 2004.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Game+Theory&rft.pages=56-57&rft.pub=UCLA+Department+of+Mathematics&rft.aulast=Ferguson&rft.aufirst=Thomas+S.&rft_id=https%3A%2F%2Fwww.math.ucla.edu%2F~tom%2FGame_Theory%2Fmat.pdf%23page%3D56&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGame+theory" class="Z3988"></span></span> </li> <li id="cite_note-25"><span class="mw-cite-backlink"><b><a href="#cite_ref-25">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFMycielski1992" class="citation book cs1"><a href="/wiki/Jan_Mycielski" title="Jan Mycielski">Mycielski, Jan</a> (1992). 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Vol. 1. pp. 41–70. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1016%2FS1574-0005%2805%2980006-2">10.1016/S1574-0005(05)80006-2</a>. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-4448-8098-7" title="Special:BookSources/978-0-4448-8098-7"><bdi>978-0-4448-8098-7</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=Games+with+Perfect+Information&rft.btitle=Handbook+of+Game+Theory+with+Economic+Applications&rft.pages=41-70&rft.date=1992&rft_id=info%3Adoi%2F10.1016%2FS1574-0005%2805%2980006-2&rft.isbn=978-0-4448-8098-7&rft.aulast=Mycielski&rft.aufirst=Jan&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGame+theory" class="Z3988"></span></span> </li> <li id="cite_note-26"><span class="mw-cite-backlink"><b><a href="#cite_ref-26">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://ghostarchive.org/varchive/youtube/20211028/PN-I6u-AxMg">"Infinite Chess"</a>. <i>PBS Infinite Series</i>. 2 March 2017. Archived from <a rel="nofollow" class="external text" href="https://www.youtube.com/watch?v=PN-I6u-AxMg&t=0m25s">the original</a> on 28 October 2021.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=PBS+Infinite+Series&rft.atitle=Infinite+Chess&rft.date=2017-03-02&rft_id=https%3A%2F%2Fwww.youtube.com%2Fwatch%3Fv%3DPN-I6u-AxMg%26t%3D0m25s&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGame+theory" class="Z3988"></span> Perfect information defined at 0:25, with academic sources <a href="/wiki/ArXiv_(identifier)" class="mw-redirect" title="ArXiv (identifier)">arXiv</a>:<a rel="nofollow" class="external text" href="https://arxiv.org/abs/1302.4377">1302.4377</a> and <a href="/wiki/ArXiv_(identifier)" class="mw-redirect" title="ArXiv (identifier)">arXiv</a>:<a rel="nofollow" class="external text" href="https://arxiv.org/abs/1510.08155">1510.08155</a>.</span> </li> <li id="cite_note-27"><span class="mw-cite-backlink"><b><a href="#cite_ref-27">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFOwen1995" class="citation book cs1">Owen, Guillermo (1995). <i>Game Theory: Third Edition</i>. Bingley: Emerald Group Publishing. p. 4. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-12-531151-9" title="Special:BookSources/978-0-12-531151-9"><bdi>978-0-12-531151-9</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Game+Theory%3A+Third+Edition&rft.place=Bingley&rft.pages=4&rft.pub=Emerald+Group+Publishing&rft.date=1995&rft.isbn=978-0-12-531151-9&rft.aulast=Owen&rft.aufirst=Guillermo&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGame+theory" class="Z3988"></span></span> </li> <li id="cite_note-28"><span class="mw-cite-backlink"><b><a href="#cite_ref-28">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFMirman1989" class="citation book cs1">Mirman, Leonard J. (1989). 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A K Peters, Ltd. pp. ix–xii. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-1-56881-210-6" title="Special:BookSources/978-1-56881-210-6"><bdi>978-1-56881-210-6</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=31&rft.btitle=Luck%2C+logic%2C+and+white+lies%3A+the+mathematics+of+games&rft.pages=ix-xii&rft.pub=A+K+Peters%2C+Ltd.&rft.date=2005&rft.isbn=978-1-56881-210-6&rft.au=J%C3%B6rg+Bewersdorff&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGame+theory" class="Z3988"></span></span> </li> <li id="cite_note-34"><span class="mw-cite-backlink"><b><a href="#cite_ref-34">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFAlbertNowakowskiWolfe2007" class="citation cs2"><a href="/wiki/Michael_H._Albert" title="Michael H. Albert">Albert, Michael H.</a>; Nowakowski, Richard J.; Wolfe, David (2007), <i>Lessons in Play: In Introduction to Combinatorial Game Theory</i>, A K Peters Ltd, pp. 3–4, <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-1-56881-277-9" title="Special:BookSources/978-1-56881-277-9"><bdi>978-1-56881-277-9</bdi></a></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Lessons+in+Play%3A+In+Introduction+to+Combinatorial+Game+Theory&rft.pages=3-4&rft.pub=A+K+Peters+Ltd&rft.date=2007&rft.isbn=978-1-56881-277-9&rft.aulast=Albert&rft.aufirst=Michael+H.&rft.au=Nowakowski%2C+Richard+J.&rft.au=Wolfe%2C+David&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGame+theory" class="Z3988"></span></span> </li> <li id="cite_note-35"><span class="mw-cite-backlink"><b><a href="#cite_ref-35">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFBeck2008" class="citation book cs1"><a href="/wiki/J%C3%B3zsef_Beck" title="József Beck">Beck, József</a> (2008). <a href="/wiki/Combinatorial_Games:_Tic-Tac-Toe_Theory" title="Combinatorial Games: Tic-Tac-Toe Theory"><i>Combinatorial Games: Tic-Tac-Toe Theory</i></a>. 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Springer, Cham. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-3-319-11832-1" title="Special:BookSources/978-3-319-11832-1"><bdi>978-3-319-11832-1</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=A+Game-Theoretical+Approach+to+Markov+Decision+Processes%2C+Stochastic+Positional+Games+and+Multicriteria+Control+Models&rft.pub=Springer%2C+Cham&rft.date=2015&rft.isbn=978-3-319-11832-1&rft.aulast=Lozovanu&rft.aufirst=D&rft.au=Pickl%2C+S&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGame+theory" class="Z3988"></span></span> </li> <li id="cite_note-FOOTNOTEOsborneRubinstein1994-42"><span class="mw-cite-backlink"><b><a href="#cite_ref-FOOTNOTEOsborneRubinstein1994_42-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFOsborneRubinstein1994">Osborne & Rubinstein (1994)</a>.</span> </li> <li id="cite_note-McMahan-43"><span class="mw-cite-backlink">^ <a href="#cite_ref-McMahan_43-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-McMahan_43-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFMcMahan2006" class="citation thesis cs1">McMahan, Hugh Brendan (2006). <a rel="nofollow" class="external text" href="https://www.cs.cmu.edu/~mcmahan/research/mcmahan_thesis.pdf"><i>Robust Planning in Domains with Stochastic Outcomes, Adversaries, and Partial Observability</i></a> <span class="cs1-format">(PDF)</span> (PhD dissertation). Carnegie Mellon University. pp. 3–4. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20110401124804/http://www.cs.cmu.edu/~mcmahan/research/mcmahan_thesis.pdf">Archived</a> <span class="cs1-format">(PDF)</span> from the original on 1 April 2011.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Adissertation&rft.title=Robust+Planning+in+Domains+with+Stochastic+Outcomes%2C+Adversaries%2C+and+Partial+Observability&rft.inst=Carnegie+Mellon+University&rft.date=2006&rft.aulast=McMahan&rft.aufirst=Hugh+Brendan&rft_id=https%3A%2F%2Fwww.cs.cmu.edu%2F~mcmahan%2Fresearch%2Fmcmahan_thesis.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGame+theory" class="Z3988"></span></span> </li> <li id="cite_note-FOOTNOTEHoward1971-44"><span class="mw-cite-backlink"><b><a href="#cite_ref-FOOTNOTEHoward1971_44-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFHoward1971">Howard (1971)</a>.</span> </li> <li id="cite_note-r7a-45"><span class="mw-cite-backlink">^ <a href="#cite_ref-r7a_45-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-r7a_45-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFRasmusen2007" class="citation book cs1">Rasmusen, Eric (2007). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=5XEMuJwnBmUC&pg=PR5"><i>Games and Information</i></a> (4th ed.). Wiley. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-1-4051-3666-2" title="Special:BookSources/978-1-4051-3666-2"><bdi>978-1-4051-3666-2</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Games+and+Information&rft.edition=4th&rft.pub=Wiley&rft.date=2007&rft.isbn=978-1-4051-3666-2&rft.aulast=Rasmusen&rft.aufirst=Eric&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3D5XEMuJwnBmUC%26pg%3DPR5&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGame+theory" class="Z3988"></span></span> </li> <li id="cite_note-r7b-46"><span class="mw-cite-backlink">^ <a href="#cite_ref-r7b_46-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-r7b_46-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFKreps1990" class="citation book cs1"><a href="/wiki/David_M._Kreps" title="David M. Kreps">Kreps, David M.</a> (1990). <i>Game Theory and Economic Modelling</i>. Oxford University Press. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1093%2F0198283814.001.0001">10.1093/0198283814.001.0001</a>. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-19-828381-2" title="Special:BookSources/978-0-19-828381-2"><bdi>978-0-19-828381-2</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Game+Theory+and+Economic+Modelling&rft.pub=Oxford+University+Press&rft.date=1990&rft_id=info%3Adoi%2F10.1093%2F0198283814.001.0001&rft.isbn=978-0-19-828381-2&rft.aulast=Kreps&rft.aufirst=David+M.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGame+theory" class="Z3988"></span><sup class="noprint Inline-Template" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Citing_sources" title="Wikipedia:Citing sources"><span title="This citation requires a reference to the specific page or range of pages in which the material appears. (July 2024)">page needed</span></a></i>]</sup></span> </li> <li id="cite_note-r7c-47"><span class="mw-cite-backlink">^ <a href="#cite_ref-r7c_47-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-r7c_47-1"><sup><i><b>b</b></i></sup></a> <a href="#cite_ref-r7c_47-2"><sup><i><b>c</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFAumannHart1992" class="citation book cs1">Aumann, R. J.; Hart, S., eds. (1992). <i>Handbook of Game Theory with Economic Applications</i>. Elsevier. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-444-89427-4" title="Special:BookSources/978-0-444-89427-4"><bdi>978-0-444-89427-4</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Handbook+of+Game+Theory+with+Economic+Applications&rft.pub=Elsevier&rft.date=1992&rft.isbn=978-0-444-89427-4&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGame+theory" class="Z3988"></span><sup class="noprint Inline-Template" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Citing_sources" title="Wikipedia:Citing sources"><span title="This citation requires a reference to the specific page or range of pages in which the material appears. (July 2024)">page needed</span></a></i>]</sup></span> </li> <li id="cite_note-r7d-48"><span class="mw-cite-backlink">^ <a href="#cite_ref-r7d_48-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-r7d_48-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFAumannHeifetz2002" class="citation book cs1">Aumann, Robert J.; Heifetz, Aviad (2002). "Chapter 43 Incomplete information". <i>Handbook of Game Theory with Economic Applications Volume 3</i>. 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(July 2024)">page needed</span></a></i>]</sup></span> </li> <li id="cite_note-93"><span class="mw-cite-backlink"><b><a href="#cite_ref-93">^</a></b></span> <span class="reference-text">Vincent P. Crawford (1997). "Theory and Experiment in the Analysis of Strategic Interaction," in <i>Advances in Economics and Econometrics: Theory and Applications</i>, pp. <a rel="nofollow" class="external text" href="http://weber.ucsd.edu/~vcrawfor/CrawfordThExp97.pdf">206–242</a> <a rel="nofollow" class="external text" href="https://web.archive.org/web/20120401234518/http://weber.ucsd.edu/~vcrawfor/CrawfordThExp97.pdf">Archived</a> 1 April 2012 at the <a href="/wiki/Wayback_Machine" title="Wayback Machine">Wayback Machine</a>. Cambridge. Reprinted in Colin F. Camerer <i>et al</i>., ed. 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"behavioural economics and game theory." <a rel="nofollow" class="external text" href="http://www.dictionaryofeconomics.com/article?id=pde2008_G000210&q=Behavioral%20economics%20&topicid=&result_number=2">Abstract.</a> <a rel="nofollow" class="external text" href="https://web.archive.org/web/20170807112808/http://www.dictionaryofeconomics.com/article?id=pde2008_G000210&q=Behavioral%20economics%20&topicid=&result_number=2">Archived</a> 7 August 2017 at the <a href="/wiki/Wayback_Machine" title="Wayback Machine">Wayback Machine</a></span> </li> <li id="cite_note-96"><span class="mw-cite-backlink"><b><a href="#cite_ref-96">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFCamerer2008" class="citation book cs1"><a href="/wiki/Colin_F._Camerer" class="mw-redirect" title="Colin F. 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Retrieved <span class="nowrap">4 August</span> 2011</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=behavioral+game+theory&rft.btitle=The+New+Palgrave+Dictionary+of+Economics&rft.date=2008&rft.aulast=Camerer&rft.aufirst=Colin+F.&rft_id=http%3A%2F%2Fwww.dictionaryofeconomics.com%2Farticle%3Fid%3Dpde2008_B000302%26q%3DBehavioral%2520economics%2520%26topicid%3D%26result_number%3D13&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGame+theory" class="Z3988"></span></span> </li> <li id="cite_note-97"><span class="mw-cite-backlink"><b><a href="#cite_ref-97">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFCamerer1997" class="citation journal cs1"><a href="/wiki/Colin_F._Camerer" class="mw-redirect" title="Colin F. Camerer">Camerer, Colin F.</a> (1997). <a rel="nofollow" class="external text" href="https://resolver.caltech.edu/CaltechAUTHORS:20110211-074641387">"Progress in Behavioral Game Theory"</a>. <i>Journal of Economic Perspectives</i>. <b>11</b> (4): 172. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1257%2Fjep.11.4.167">10.1257/jep.11.4.167</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Journal+of+Economic+Perspectives&rft.atitle=Progress+in+Behavioral+Game+Theory&rft.volume=11&rft.issue=4&rft.pages=172&rft.date=1997&rft_id=info%3Adoi%2F10.1257%2Fjep.11.4.167&rft.aulast=Camerer&rft.aufirst=Colin+F.&rft_id=https%3A%2F%2Fresolver.caltech.edu%2FCaltechAUTHORS%3A20110211-074641387&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGame+theory" class="Z3988"></span></span> </li> <li id="cite_note-98"><span class="mw-cite-backlink"><b><a href="#cite_ref-98">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFCamerer2003" class="citation book cs1"><a href="/wiki/Colin_F._Camerer" class="mw-redirect" title="Colin F. Camerer">Camerer, Colin F.</a> (2003). <i>Behavioral Game Theory</i>. Princeton.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Behavioral+Game+Theory&rft.pub=Princeton&rft.date=2003&rft.aulast=Camerer&rft.aufirst=Colin+F.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGame+theory" class="Z3988"></span> <a rel="nofollow" class="external text" href="http://press.princeton.edu/chapters/i7517.html">Description</a> <a rel="nofollow" class="external text" href="https://web.archive.org/web/20110514201411/http://press.princeton.edu/chapters/i7517.html">Archived</a> 14 May 2011 at the <a href="/wiki/Wayback_Machine" title="Wayback Machine">Wayback Machine</a>, <a rel="nofollow" class="external text" href="https://books.google.com/books?id=cr_Xg7cRvdcC&pg=PR7">preview</a> <a rel="nofollow" class="external text" href="https://web.archive.org/web/20230326164811/https://books.google.com/books?id=cr_Xg7cRvdcC&pg=PR7">Archived</a> 26 March 2023 at the <a href="/wiki/Wayback_Machine" title="Wayback Machine">Wayback Machine</a> ([ctrl]+), and ch. 1 <a rel="nofollow" class="external text" href="http://press.princeton.edu/chapters/i7517.pdf">link</a> <a rel="nofollow" class="external text" href="https://web.archive.org/web/20130704185133/http://press.princeton.edu/chapters/i7517.pdf">Archived</a> 4 July 2013 at the <a href="/wiki/Wayback_Machine" title="Wayback Machine">Wayback Machine</a>.</span> </li> <li id="cite_note-99"><span class="mw-cite-backlink"><b><a href="#cite_ref-99">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFCamererLoewensteinRabin2011" class="citation book cs1">Camerer, Colin F.; Loewenstein, George; Rabin, Matthew, eds. 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(July 2024)">page needed</span></a></i>]</sup></span> </li> <li id="cite_note-100"><span class="mw-cite-backlink"><b><a href="#cite_ref-100">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFFudenberg2006" class="citation journal cs1"><a href="/wiki/Drew_Fudenberg" title="Drew Fudenberg">Fudenberg, Drew</a> (2006). <a rel="nofollow" class="external text" href="http://nrs.harvard.edu/urn-3:HUL.InstRepos:3208222">"Advancing Beyond Advances in Behavioral Economics"</a>. <i>Journal of Economic Literature</i>. <b>44</b> (3): 694–711. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1257%2Fjel.44.3.694">10.1257/jel.44.3.694</a>. <a href="/wiki/JSTOR_(identifier)" class="mw-redirect" title="JSTOR (identifier)">JSTOR</a> <a rel="nofollow" class="external text" href="https://www.jstor.org/stable/30032349">30032349</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:3490729">3490729</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Journal+of+Economic+Literature&rft.atitle=Advancing+Beyond+Advances+in+Behavioral+Economics&rft.volume=44&rft.issue=3&rft.pages=694-711&rft.date=2006&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A3490729%23id-name%3DS2CID&rft_id=https%3A%2F%2Fwww.jstor.org%2Fstable%2F30032349%23id-name%3DJSTOR&rft_id=info%3Adoi%2F10.1257%2Fjel.44.3.694&rft.aulast=Fudenberg&rft.aufirst=Drew&rft_id=http%3A%2F%2Fnrs.harvard.edu%2Furn-3%3AHUL.InstRepos%3A3208222&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGame+theory" class="Z3988"></span></span> </li> <li id="cite_note-101"><span class="mw-cite-backlink"><b><a href="#cite_ref-101">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFTirole1988" class="citation book cs1"><a href="/wiki/Jean_Tirole" title="Jean Tirole">Tirole, Jean</a> (1988). <i>The Theory of Industrial Organization</i>. 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(July 2024)">page needed</span></a></i>]</sup></span> </li> <li id="cite_note-133"><span class="mw-cite-backlink"><b><a href="#cite_ref-133">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFParashar2022" class="citation news cs1">Parashar, Nilesh (15 August 2022). <a rel="nofollow" class="external text" href="https://medium.com/@niitwork0921/what-is-game-theory-in-ai-6b7c4c383f03">"What is Game Theory in AI?"</a>. <i>Medium</i>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Medium&rft.atitle=What+is+Game+Theory+in+AI%3F&rft.date=2022-08-15&rft.aulast=Parashar&rft.aufirst=Nilesh&rft_id=https%3A%2F%2Fmedium.com%2F%40niitwork0921%2Fwhat-is-game-theory-in-ai-6b7c4c383f03&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGame+theory" class="Z3988"></span></span> </li> <li id="cite_note-134"><span class="mw-cite-backlink"><b><a href="#cite_ref-134">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFHazraAnjaria2022" class="citation journal cs1">Hazra, Tanmoy; Anjaria, Kushal (March 2022). <a rel="nofollow" class="external text" href="https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9039031">"Applications of game theory in deep learning: a survey"</a>. <i>Multimedia Tools and Applications</i>. <b>81</b> (6): 8963–8994. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1007%2Fs11042-022-12153-2">10.1007/s11042-022-12153-2</a>. <a href="/wiki/PMC_(identifier)" class="mw-redirect" title="PMC (identifier)">PMC</a> <span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9039031">9039031</a></span>. <a href="/wiki/PMID_(identifier)" class="mw-redirect" title="PMID (identifier)">PMID</a> <a rel="nofollow" class="external text" href="https://pubmed.ncbi.nlm.nih.gov/35496996">35496996</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Multimedia+Tools+and+Applications&rft.atitle=Applications+of+game+theory+in+deep+learning%3A+a+survey&rft.volume=81&rft.issue=6&rft.pages=8963-8994&rft.date=2022-03&rft_id=https%3A%2F%2Fwww.ncbi.nlm.nih.gov%2Fpmc%2Farticles%2FPMC9039031%23id-name%3DPMC&rft_id=info%3Apmid%2F35496996&rft_id=info%3Adoi%2F10.1007%2Fs11042-022-12153-2&rft.aulast=Hazra&rft.aufirst=Tanmoy&rft.au=Anjaria%2C+Kushal&rft_id=https%3A%2F%2Fwww.ncbi.nlm.nih.gov%2Fpmc%2Farticles%2FPMC9039031&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGame+theory" class="Z3988"></span></span> </li> <li id="cite_note-135"><span class="mw-cite-backlink"><b><a href="#cite_ref-135">^</a></b></span> <span class="reference-text"><a href="#CITEREFSkyrms1996">Skyrms (1996)</a></span> </li> <li id="cite_note-FOOTNOTEGrimKokalisAlai-TaftiKilb2004-136"><span class="mw-cite-backlink"><b><a href="#cite_ref-FOOTNOTEGrimKokalisAlai-TaftiKilb2004_136-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFGrimKokalisAlai-TaftiKilb2004">Grim et al. 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(July 2024)">page needed</span></a></i>]</sup></span> </li> <li id="cite_note-138"><span class="mw-cite-backlink"><b><a href="#cite_ref-138">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFBicchieri2006" class="citation cs2"><a href="/wiki/Cristina_Bicchieri" title="Cristina Bicchieri">Bicchieri, Cristina</a> (2006), <i>The Grammar of Society: the Nature and Dynamics of Social Norms</i>, Cambridge University Press, <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-521-57372-6" title="Special:BookSources/978-0-521-57372-6"><bdi>978-0-521-57372-6</bdi></a></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=The+Grammar+of+Society%3A+the+Nature+and+Dynamics+of+Social+Norms&rft.pub=Cambridge+University+Press&rft.date=2006&rft.isbn=978-0-521-57372-6&rft.aulast=Bicchieri&rft.aufirst=Cristina&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGame+theory" class="Z3988"></span><sup class="noprint Inline-Template" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Citing_sources" title="Wikipedia:Citing sources"><span title="This citation requires a reference to the specific page or range of pages in which the material appears. (July 2024)">page needed</span></a></i>]</sup></span> </li> <li id="cite_note-139"><span class="mw-cite-backlink"><b><a href="#cite_ref-139">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFBicchieri1989" class="citation journal cs1"><a href="/wiki/Cristina_Bicchieri" title="Cristina Bicchieri">Bicchieri, Cristina</a> (1989). 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(July 2024)">page needed</span></a></i>]</sup></span> </li> <li id="cite_note-144"><span class="mw-cite-backlink"><b><a href="#cite_ref-144">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFKuhn2004" class="citation journal cs1">Kuhn, Steven T. (July 2004). 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Retrieved <span class="nowrap">25 July</span> 2018</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Pacific+Sun&rft.atitle=Star+on+hold%3A+Faithful+following%2C+meager+sales&rft.date=1996-03-06&rft.aulast=Guzman&rft.aufirst=Rafer&rft_id=http%3A%2F%2Fwww.loudfamily.com%2Fold%2Fintpacsun.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGame+theory" class="Z3988"></span>.</span> </li> <li id="cite_note-163"><span class="mw-cite-backlink"><b><a href="#cite_ref-163">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://www.animenewsnetwork.com/encyclopedia/manga.php?id=8178">"Liar Game (manga) – Anime News Network"</a>. <i>www.animenewsnetwork.com</i>. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20221125140852/https://www.animenewsnetwork.com/encyclopedia/manga.php?id=8178">Archived</a> from the original on 25 November 2022<span class="reference-accessdate">. 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PokerNews.com. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20221105190628/https://www.pokernews.com/news/2018/08/poker-and-game-theory-featured-in-hit-film-crazy-rich-asians-31847.htm">Archived</a> from the original on 5 November 2022<span class="reference-accessdate">. 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Retrieved <span class="nowrap">5 November</span> 2022</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Game+theory+in+Crazy+Rich+Asians%3A+explaining+the+Mahjong+showdown+between+Rachel+and+Eleanor&rft.pub=Colossus&rft.date=2019-02-08&rft.aulast=Bean&rft.aufirst=Travis&rft_id=https%3A%2F%2Ffilmcolossus.com%2Fcrazy-rich-asians-game-theory%2F&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGame+theory" class="Z3988"></span></span> </li> <li id="cite_note-166"><span class="mw-cite-backlink"><b><a href="#cite_ref-166">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://blogs.cornell.edu/info2040/2022/10/25/an-analysis-of-the-applications-of-networks-in-mollys-game/">"An Analysis of the Applications of Networks in "Molly's Game" : Networks Course blog for INFO 2040/CS 2850/Econ 2040/SOC 2090"</a>. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20230408025922/https://blogs.cornell.edu/info2040/2022/10/25/an-analysis-of-the-applications-of-networks-in-mollys-game/">Archived</a> from the original on 8 April 2023<span class="reference-accessdate">. Retrieved <span class="nowrap">8 April</span> 2023</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=An+Analysis+of+the+Applications+of+Networks+in+%22Molly%27s+Game%22+%3A+Networks+Course+blog+for+INFO+2040%2FCS+2850%2FEcon+2040%2FSOC+2090&rft_id=https%3A%2F%2Fblogs.cornell.edu%2Finfo2040%2F2022%2F10%2F25%2Fan-analysis-of-the-applications-of-networks-in-mollys-game%2F&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGame+theory" class="Z3988"></span></span> </li> </ol></div></div> <div class="mw-heading mw-heading2"><h2 id="Sources">Sources</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Game_theory&action=edit&section=48" title="Edit section: Sources"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFBen-DavidBorodinKarpTardos1994" class="citation journal cs1">Ben-David, S.; Borodin, A.; Karp, R.; Tardos, G.; Wigderson, A. (January 1994). "On the power of randomization in on-line algorithms". <i>Algorithmica</i>. <b>11</b> (1): 2–14. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1007%2FBF01294260">10.1007/BF01294260</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:26771869">26771869</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Algorithmica&rft.atitle=On+the+power+of+randomization+in+on-line+algorithms&rft.volume=11&rft.issue=1&rft.pages=2-14&rft.date=1994-01&rft_id=info%3Adoi%2F10.1007%2FBF01294260&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A26771869%23id-name%3DS2CID&rft.aulast=Ben-David&rft.aufirst=S.&rft.au=Borodin%2C+A.&rft.au=Karp%2C+R.&rft.au=Tardos%2C+G.&rft.au=Wigderson%2C+A.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGame+theory" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFDowns1957" class="citation cs2"><a href="/wiki/Anthony_Downs" title="Anthony Downs">Downs, Anthony</a> (1957), <a href="/wiki/An_Economic_Theory_of_Democracy" title="An Economic Theory of Democracy"><i>An Economic theory of Democracy</i></a>, New York: Harper</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=An+Economic+theory+of+Democracy&rft.place=New+York&rft.pub=Harper&rft.date=1957&rft.aulast=Downs&rft.aufirst=Anthony&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGame+theory" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFFisher1930" class="citation book cs1">Fisher, Sir Ronald Aylmer (1930). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=t3jwAAAAMAAJ"><i>The Genetical Theory of Natural Selection</i></a>. Clarendon Press.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=The+Genetical+Theory+of+Natural+Selection&rft.pub=Clarendon+Press&rft.date=1930&rft.aulast=Fisher&rft.aufirst=Sir+Ronald+Aylmer&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3Dt3jwAAAAMAAJ&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGame+theory" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFGauthier1986" class="citation cs2"><a href="/wiki/David_Gauthier" title="David Gauthier">Gauthier, David</a> (1986), <i>Morals by agreement</i>, <a href="/wiki/Oxford_University_Press" title="Oxford University Press">Oxford University Press</a>, <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-19-824992-4" title="Special:BookSources/978-0-19-824992-4"><bdi>978-0-19-824992-4</bdi></a></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Morals+by+agreement&rft.pub=Oxford+University+Press&rft.date=1986&rft.isbn=978-0-19-824992-4&rft.aulast=Gauthier&rft.aufirst=David&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGame+theory" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFGrimKokalisAlai-TaftiKilb2004" class="citation cs2">Grim, Patrick; Kokalis, Trina; Alai-Tafti, Ali; Kilb, Nicholas; St Denis, Paul (2004), "Making meaning happen", <i>Journal of Experimental & Theoretical Artificial Intelligence</i>, <b>16</b> (4): 209–243, <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1080%2F09528130412331294715">10.1080/09528130412331294715</a>, <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:5737352">5737352</a></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Journal+of+Experimental+%26+Theoretical+Artificial+Intelligence&rft.atitle=Making+meaning+happen&rft.volume=16&rft.issue=4&rft.pages=209-243&rft.date=2004&rft_id=info%3Adoi%2F10.1080%2F09528130412331294715&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A5737352%23id-name%3DS2CID&rft.aulast=Grim&rft.aufirst=Patrick&rft.au=Kokalis%2C+Trina&rft.au=Alai-Tafti%2C+Ali&rft.au=Kilb%2C+Nicholas&rft.au=St+Denis%2C+Paul&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGame+theory" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFHarperMaynard_Smith2003" class="citation cs2"><a href="/wiki/David_Harper_(biologist)" title="David Harper (biologist)">Harper, David</a>; <a href="/wiki/John_Maynard_Smith" title="John Maynard Smith">Maynard Smith, John</a> (2003), <i>Animal signals</i>, Oxford University Press, <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-19-852685-8" title="Special:BookSources/978-0-19-852685-8"><bdi>978-0-19-852685-8</bdi></a></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Animal+signals&rft.pub=Oxford+University+Press&rft.date=2003&rft.isbn=978-0-19-852685-8&rft.aulast=Harper&rft.aufirst=David&rft.au=Maynard+Smith%2C+John&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGame+theory" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFHoward1971" class="citation cs2">Howard, Nigel (1971), <i>Paradoxes of Rationality: Games, Metagames, and Political Behavior</i>, Cambridge, <a href="/wiki/Massachusetts" title="Massachusetts">MA</a>: The MIT Press, <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-262-58237-7" title="Special:BookSources/978-0-262-58237-7"><bdi>978-0-262-58237-7</bdi></a></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Paradoxes+of+Rationality%3A+Games%2C+Metagames%2C+and+Political+Behavior&rft.place=Cambridge%2C+MA&rft.pub=The+MIT+Press&rft.date=1971&rft.isbn=978-0-262-58237-7&rft.aulast=Howard&rft.aufirst=Nigel&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGame+theory" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFKavka1986" class="citation book cs1">Kavka, Gregory S. (1986). <i>Hobbesian Moral and Political Theory</i>. Princeton University Press. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-691-02765-4" title="Special:BookSources/978-0-691-02765-4"><bdi>978-0-691-02765-4</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Hobbesian+Moral+and+Political+Theory&rft.pub=Princeton+University+Press&rft.date=1986&rft.isbn=978-0-691-02765-4&rft.aulast=Kavka&rft.aufirst=Gregory+S.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGame+theory" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFLewis1969" class="citation cs2"><a href="/wiki/David_Kellogg_Lewis" class="mw-redirect" title="David Kellogg Lewis">Lewis, David</a> (1969), <i>Convention: A Philosophical Study</i></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Convention%3A+A+Philosophical+Study&rft.date=1969&rft.aulast=Lewis&rft.aufirst=David&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGame+theory" class="Z3988"></span>, <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-631-23257-5" title="Special:BookSources/978-0-631-23257-5">978-0-631-23257-5</a> (2002 edition)</li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFMaynard_SmithPrice1973" class="citation cs2"><a href="/wiki/John_Maynard_Smith" title="John Maynard Smith">Maynard Smith, John</a>; <a href="/wiki/George_R._Price" title="George R. Price">Price, George R.</a> (1973), "The logic of animal conflict", <i>Nature</i>, <b>246</b> (5427): 15–18, <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1973Natur.246...15S">1973Natur.246...15S</a>, <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1038%2F246015a0">10.1038/246015a0</a>, <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:4224989">4224989</a></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Nature&rft.atitle=The+logic+of+animal+conflict&rft.volume=246&rft.issue=5427&rft.pages=15-18&rft.date=1973&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A4224989%23id-name%3DS2CID&rft_id=info%3Adoi%2F10.1038%2F246015a0&rft_id=info%3Abibcode%2F1973Natur.246...15S&rft.aulast=Maynard+Smith&rft.aufirst=John&rft.au=Price%2C+George+R.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGame+theory" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFOsborneRubinstein1994" class="citation cs2">Osborne, Martin J.; <a href="/wiki/Ariel_Rubinstein" title="Ariel Rubinstein">Rubinstein, Ariel</a> (1994), <i>A course in game theory</i>, MIT Press, <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-262-65040-3" title="Special:BookSources/978-0-262-65040-3"><bdi>978-0-262-65040-3</bdi></a></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=A+course+in+game+theory&rft.pub=MIT+Press&rft.date=1994&rft.isbn=978-0-262-65040-3&rft.aulast=Osborne&rft.aufirst=Martin+J.&rft.au=Rubinstein%2C+Ariel&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGame+theory" class="Z3988"></span>. A modern introduction at the graduate level.</li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFPoundstone1993" class="citation book cs1">Poundstone, William (1993). <a rel="nofollow" class="external text" href="https://archive.org/details/prisonersdilemma00poun"><i>Prisoner's Dilemma</i></a> (1st Anchor Books ed.). New York: Anchor. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-385-41580-X" title="Special:BookSources/0-385-41580-X"><bdi>0-385-41580-X</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Prisoner%27s+Dilemma&rft.place=New+York&rft.edition=1st+Anchor+Books&rft.pub=Anchor&rft.date=1993&rft.isbn=0-385-41580-X&rft.aulast=Poundstone&rft.aufirst=William&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Fprisonersdilemma00poun&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGame+theory" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFQuine1967" class="citation cs2"><a href="/wiki/Willard_Van_Orman_Quine" title="Willard Van Orman Quine">Quine, W.v.O</a> (1967), "Truth by Convention", <i>Philosophica Essays for A.N. Whitehead</i>, Russel and Russel Publishers, <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-8462-0970-6" title="Special:BookSources/978-0-8462-0970-6"><bdi>978-0-8462-0970-6</bdi></a></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=Truth+by+Convention&rft.btitle=Philosophica+Essays+for+A.N.+Whitehead&rft.pub=Russel+and+Russel+Publishers&rft.date=1967&rft.isbn=978-0-8462-0970-6&rft.aulast=Quine&rft.aufirst=W.v.O&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGame+theory" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFQuine1960" class="citation cs2"><a href="/wiki/Willard_Van_Orman_Quine" title="Willard Van Orman Quine">Quine, W.v.O</a> (1960), "Carnap and Logical Truth", <i>Synthese</i>, <b>12</b> (4): 350–374, <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1007%2FBF00485423">10.1007/BF00485423</a>, <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:46979744">46979744</a></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Synthese&rft.atitle=Carnap+and+Logical+Truth&rft.volume=12&rft.issue=4&rft.pages=350-374&rft.date=1960&rft_id=info%3Adoi%2F10.1007%2FBF00485423&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A46979744%23id-name%3DS2CID&rft.aulast=Quine&rft.aufirst=W.v.O&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGame+theory" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFSkyrms1996" class="citation cs2">Skyrms, Brian (1996), <i>Evolution of the social contract</i>, Cambridge University Press, <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-521-55583-8" title="Special:BookSources/978-0-521-55583-8"><bdi>978-0-521-55583-8</bdi></a></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Evolution+of+the+social+contract&rft.pub=Cambridge+University+Press&rft.date=1996&rft.isbn=978-0-521-55583-8&rft.aulast=Skyrms&rft.aufirst=Brian&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGame+theory" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFSkyrms2004" class="citation cs2">Skyrms, Brian (2004), <i>The stag hunt and the evolution of social structure</i>, Cambridge University Press, <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-521-53392-8" title="Special:BookSources/978-0-521-53392-8"><bdi>978-0-521-53392-8</bdi></a></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=The+stag+hunt+and+the+evolution+of+social+structure&rft.pub=Cambridge+University+Press&rft.date=2004&rft.isbn=978-0-521-53392-8&rft.aulast=Skyrms&rft.aufirst=Brian&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGame+theory" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFSoberWilson1998" class="citation cs2">Sober, Elliott; Wilson, David Sloan (1998), <i>Unto others: the evolution and psychology of unselfish behavior</i>, Harvard University Press, <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-674-93047-6" title="Special:BookSources/978-0-674-93047-6"><bdi>978-0-674-93047-6</bdi></a></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Unto+others%3A+the+evolution+and+psychology+of+unselfish+behavior&rft.pub=Harvard+University+Press&rft.date=1998&rft.isbn=978-0-674-93047-6&rft.aulast=Sober&rft.aufirst=Elliott&rft.au=Wilson%2C+David+Sloan&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGame+theory" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFWebb2007" class="citation cs2">Webb, James N. (2007), <i>Game theory: decisions, interaction and evolution</i>, Undergraduate mathematics, Springer, <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-1-84628-423-6" title="Special:BookSources/978-1-84628-423-6"><bdi>978-1-84628-423-6</bdi></a></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Game+theory%3A+decisions%2C+interaction+and+evolution&rft.series=Undergraduate+mathematics&rft.pub=Springer&rft.date=2007&rft.isbn=978-1-84628-423-6&rft.aulast=Webb&rft.aufirst=James+N.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGame+theory" class="Z3988"></span> Consistent treatment of game types usually claimed by different applied fields, e.g. <a href="/wiki/Markov_decision_process" title="Markov decision process">Markov decision processes</a>.</li></ul> <div class="mw-heading mw-heading2"><h2 id="Further_reading">Further reading</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Game_theory&action=edit&section=49" title="Edit section: Further reading"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1235681985">.mw-parser-output .side-box{margin:4px 0;box-sizing:border-box;border:1px solid #aaa;font-size:88%;line-height:1.25em;background-color:var(--background-color-interactive-subtle,#f8f9fa);display:flow-root}.mw-parser-output .side-box-abovebelow,.mw-parser-output .side-box-text{padding:0.25em 0.9em}.mw-parser-output .side-box-image{padding:2px 0 2px 0.9em;text-align:center}.mw-parser-output .side-box-imageright{padding:2px 0.9em 2px 0;text-align:center}@media(min-width:500px){.mw-parser-output .side-box-flex{display:flex;align-items:center}.mw-parser-output .side-box-text{flex:1;min-width:0}}@media(min-width:720px){.mw-parser-output .side-box{width:238px}.mw-parser-output .side-box-right{clear:right;float:right;margin-left:1em}.mw-parser-output .side-box-left{margin-right:1em}}</style><style data-mw-deduplicate="TemplateStyles:r1237033735">@media print{body.ns-0 .mw-parser-output .sistersitebox{display:none!important}}@media screen{html.skin-theme-clientpref-night .mw-parser-output .sistersitebox img[src*="Wiktionary-logo-en-v2.svg"]{background-color:white}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .sistersitebox img[src*="Wiktionary-logo-en-v2.svg"]{background-color:white}}</style><div class="side-box side-box-right plainlinks sistersitebox"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1126788409"> <div class="side-box-flex"> <div class="side-box-image"><span class="noviewer" typeof="mw:File"><span><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/f/fa/Wikiquote-logo.svg/34px-Wikiquote-logo.svg.png" decoding="async" width="34" height="40" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/f/fa/Wikiquote-logo.svg/51px-Wikiquote-logo.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/f/fa/Wikiquote-logo.svg/68px-Wikiquote-logo.svg.png 2x" data-file-width="300" data-file-height="355" /></span></span></div> <div class="side-box-text plainlist">Wikiquote has quotations related to <i><b><a href="https://en.wikiquote.org/wiki/Special:Search/Game_theory" class="extiw" title="q:Special:Search/Game theory">Game theory</a></b></i>.</div></div> </div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1235681985"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1237033735"><div class="side-box side-box-right plainlinks sistersitebox"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1126788409"> <div class="side-box-flex"> <div class="side-box-image"><span class="noviewer" typeof="mw:File"><span><img alt="" src="//upload.wikimedia.org/wikipedia/en/thumb/4/4a/Commons-logo.svg/30px-Commons-logo.svg.png" decoding="async" width="30" height="40" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/4/4a/Commons-logo.svg/45px-Commons-logo.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/4/4a/Commons-logo.svg/59px-Commons-logo.svg.png 2x" data-file-width="1024" data-file-height="1376" /></span></span></div> <div class="side-box-text plainlist">Wikimedia Commons has media related to <span style="font-weight: bold; font-style: italic;"><a href="https://commons.wikimedia.org/wiki/Category:Game_theory" class="extiw" title="commons:Category:Game theory">Game theory</a></span>.</div></div> </div> <div class="mw-heading mw-heading3"><h3 id="Textbooks_and_general_literature">Textbooks and general literature</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Game_theory&action=edit&section=50" title="Edit section: Textbooks and general literature"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFAumann1987" class="citation cs2"><a href="/wiki/Robert_Aumann" title="Robert Aumann">Aumann, Robert J</a> (1987), "game theory", <a href="/wiki/The_New_Palgrave:_A_Dictionary_of_Economics" class="mw-redirect" title="The New Palgrave: A Dictionary of Economics"><i>The New Palgrave: A Dictionary of Economics</i></a>, vol. 2, pp. 460–82</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=game+theory&rft.btitle=The+New+Palgrave%3A+A+Dictionary+of+Economics&rft.pages=460-82&rft.date=1987&rft.aulast=Aumann&rft.aufirst=Robert+J&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGame+theory" class="Z3988"></span>.</li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFCamerer2003" class="citation cs2"><a href="/wiki/Colin_Camerer" title="Colin Camerer">Camerer, Colin</a> (2003), <a rel="nofollow" class="external text" href="https://web.archive.org/web/20110514201411/http://press.princeton.edu/chapters/i7517.html">"Introduction"</a>, <i>Behavioral Game Theory: Experiments in Strategic Interaction</i>, Russell Sage Foundation, pp. 1–25, <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-691-09039-9" title="Special:BookSources/978-0-691-09039-9"><bdi>978-0-691-09039-9</bdi></a>, archived from <a rel="nofollow" class="external text" href="http://press.princeton.edu/chapters/i7517.html">the original</a> on 14 May 2011<span class="reference-accessdate">, retrieved <span class="nowrap">9 February</span> 2011</span></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=Introduction&rft.btitle=Behavioral+Game+Theory%3A+Experiments+in+Strategic+Interaction&rft.pages=1-25&rft.pub=Russell+Sage+Foundation&rft.date=2003&rft.isbn=978-0-691-09039-9&rft.aulast=Camerer&rft.aufirst=Colin&rft_id=http%3A%2F%2Fpress.princeton.edu%2Fchapters%2Fi7517.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGame+theory" class="Z3988"></span>, <a rel="nofollow" class="external text" href="http://press.princeton.edu/titles/7517.html">Description</a>.</li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFDutta1999" class="citation cs2">Dutta, Prajit K. (1999), <i>Strategies and games: theory and practice</i>, <a href="/wiki/MIT_Press" title="MIT Press">MIT Press</a>, <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-262-04169-0" title="Special:BookSources/978-0-262-04169-0"><bdi>978-0-262-04169-0</bdi></a></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Strategies+and+games%3A+theory+and+practice&rft.pub=MIT+Press&rft.date=1999&rft.isbn=978-0-262-04169-0&rft.aulast=Dutta&rft.aufirst=Prajit+K.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGame+theory" class="Z3988"></span>. Suitable for undergraduate and business students.</li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFFernandezBierman1998" class="citation cs2">Fernandez, L F.; Bierman, H S. (1998), <i>Game theory with economic applications</i>, <a href="/wiki/Addison-Wesley" title="Addison-Wesley">Addison-Wesley</a>, <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-201-84758-1" title="Special:BookSources/978-0-201-84758-1"><bdi>978-0-201-84758-1</bdi></a></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Game+theory+with+economic+applications&rft.pub=Addison-Wesley&rft.date=1998&rft.isbn=978-0-201-84758-1&rft.aulast=Fernandez&rft.aufirst=L+F.&rft.au=Bierman%2C+H+S.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGame+theory" class="Z3988"></span>. Suitable for upper-level undergraduates.</li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFGaffalPadilla_Gálvez2014" class="citation book cs1">Gaffal, Margit; Padilla Gálvez, Jesús (2014). <i>Dynamics of Rational Negotiation: Game Theory, Language Games and Forms of Life</i>. Springer.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Dynamics+of+Rational+Negotiation%3A+Game+Theory%2C+Language+Games+and+Forms+of+Life&rft.pub=Springer&rft.date=2014&rft.aulast=Gaffal&rft.aufirst=Margit&rft.au=Padilla+G%C3%A1lvez%2C+Jes%C3%BAs&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGame+theory" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFGibbons1992" class="citation cs2">Gibbons, Robert D. (1992), <i>Game theory for applied economists</i>, Princeton University Press, <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-691-00395-5" title="Special:BookSources/978-0-691-00395-5"><bdi>978-0-691-00395-5</bdi></a></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Game+theory+for+applied+economists&rft.pub=Princeton+University+Press&rft.date=1992&rft.isbn=978-0-691-00395-5&rft.aulast=Gibbons&rft.aufirst=Robert+D.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGame+theory" class="Z3988"></span>. Suitable for advanced undergraduates. <ul><li>Published in Europe as <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFGibbons2001" class="citation cs2">Gibbons, Robert (2001), <i>A Primer in Game Theory</i>, London: Harvester Wheatsheaf, <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-7450-1159-2" title="Special:BookSources/978-0-7450-1159-2"><bdi>978-0-7450-1159-2</bdi></a></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=A+Primer+in+Game+Theory&rft.place=London&rft.pub=Harvester+Wheatsheaf&rft.date=2001&rft.isbn=978-0-7450-1159-2&rft.aulast=Gibbons&rft.aufirst=Robert&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGame+theory" class="Z3988"></span>.</li></ul></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFGintis2000" class="citation cs2">Gintis, Herbert (2000), <i>Game theory evolving: a problem-centered introduction to modeling strategic behavior</i>, Princeton University Press, <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-691-00943-8" title="Special:BookSources/978-0-691-00943-8"><bdi>978-0-691-00943-8</bdi></a></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Game+theory+evolving%3A+a+problem-centered+introduction+to+modeling+strategic+behavior&rft.pub=Princeton+University+Press&rft.date=2000&rft.isbn=978-0-691-00943-8&rft.aulast=Gintis&rft.aufirst=Herbert&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGame+theory" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFGreenMas-ColellWhinston1995" class="citation cs2">Green, Jerry R.; <a href="/wiki/Andreu_Mas-Colell" title="Andreu Mas-Colell">Mas-Colell, Andreu</a>; Whinston, Michael D. (1995), <i>Microeconomic theory</i>, <a href="/wiki/Oxford_University_Press" title="Oxford University Press">Oxford University Press</a>, <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-19-507340-9" title="Special:BookSources/978-0-19-507340-9"><bdi>978-0-19-507340-9</bdi></a></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Microeconomic+theory&rft.pub=Oxford+University+Press&rft.date=1995&rft.isbn=978-0-19-507340-9&rft.aulast=Green&rft.aufirst=Jerry+R.&rft.au=Mas-Colell%2C+Andreu&rft.au=Whinston%2C+Michael+D.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGame+theory" class="Z3988"></span>. Presents game theory in formal way suitable for graduate level.</li> <li>Joseph E. Harrington (2008) <i>Games, strategies, and decision making</i>, Worth, <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-7167-6630-2" title="Special:BookSources/0-7167-6630-2">0-7167-6630-2</a>. Textbook suitable for undergraduates in applied fields; numerous examples, fewer formalisms in concept presentation.</li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFIsaacs1999" class="citation cs2"><a href="/wiki/Rufus_Isaacs_(game_theorist)" title="Rufus Isaacs (game theorist)">Isaacs, Rufus</a> (1999), <i>Differential Games: A Mathematical Theory With Applications to Warfare and Pursuit, Control and Optimization</i>, New York: <a href="/wiki/Dover_Publications" title="Dover Publications">Dover Publications</a>, <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-486-40682-4" title="Special:BookSources/978-0-486-40682-4"><bdi>978-0-486-40682-4</bdi></a></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Differential+Games%3A+A+Mathematical+Theory+With+Applications+to+Warfare+and+Pursuit%2C+Control+and+Optimization&rft.place=New+York&rft.pub=Dover+Publications&rft.date=1999&rft.isbn=978-0-486-40682-4&rft.aulast=Isaacs&rft.aufirst=Rufus&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGame+theory" class="Z3988"></span></li> <li>Maschler, Michael; Solan, Eilon; Zamir, Shmuel (2013), <i>Game Theory</i>, Cambridge University Press, <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-1-108-49345-1" title="Special:BookSources/978-1-108-49345-1">978-1-108-49345-1</a>. Undergraduate textbook.</li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFMiller2003" class="citation cs2">Miller, James H. (2003), <i>Game theory at work: how to use game theory to outthink and outmaneuver your competition</i>, New York: <a href="/wiki/McGraw-Hill" class="mw-redirect" title="McGraw-Hill">McGraw-Hill</a>, <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-07-140020-6" title="Special:BookSources/978-0-07-140020-6"><bdi>978-0-07-140020-6</bdi></a></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Game+theory+at+work%3A+how+to+use+game+theory+to+outthink+and+outmaneuver+your+competition&rft.place=New+York&rft.pub=McGraw-Hill&rft.date=2003&rft.isbn=978-0-07-140020-6&rft.aulast=Miller&rft.aufirst=James+H.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGame+theory" class="Z3988"></span>. Suitable for a general audience.</li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFShohamLeyton-Brown2009" class="citation cs2">Shoham, Yoav; Leyton-Brown, Kevin (2009), <a rel="nofollow" class="external text" href="http://www.masfoundations.org/download.html"><i>Multiagent Systems: Algorithmic, Game-Theoretic, and Logical Foundations</i></a>, New York: Cambridge University Press, <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-521-89943-7" title="Special:BookSources/978-0-521-89943-7"><bdi>978-0-521-89943-7</bdi></a><span class="reference-accessdate">, retrieved <span class="nowrap">8 March</span> 2016</span></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Multiagent+Systems%3A+Algorithmic%2C+Game-Theoretic%2C+and+Logical+Foundations&rft.place=New+York&rft.pub=Cambridge+University+Press&rft.date=2009&rft.isbn=978-0-521-89943-7&rft.aulast=Shoham&rft.aufirst=Yoav&rft.au=Leyton-Brown%2C+Kevin&rft_id=http%3A%2F%2Fwww.masfoundations.org%2Fdownload.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGame+theory" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFWatson2013" class="citation cs2">Watson, Joel (2013), <a rel="nofollow" class="external text" href="https://wwnorton.com/books/Strategy/"><i>Strategy: An Introduction to Game Theory (3rd edition)</i></a>, New York: W.W. Norton and Co., <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-393-91838-0" title="Special:BookSources/978-0-393-91838-0"><bdi>978-0-393-91838-0</bdi></a></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Strategy%3A+An+Introduction+to+Game+Theory+%283rd+edition%29&rft.place=New+York&rft.pub=W.W.+Norton+and+Co.&rft.date=2013&rft.isbn=978-0-393-91838-0&rft.aulast=Watson&rft.aufirst=Joel&rft_id=https%3A%2F%2Fwwnorton.com%2Fbooks%2FStrategy%2F&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGame+theory" class="Z3988"></span>. A leading textbook at the advanced undergraduate level.</li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFMcCain2010" class="citation book cs1">McCain, Roger A. (2010). <i>Game Theory: A Nontechnical Introduction to the Analysis of Strategy</i>. World Scientific. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-981-4289-65-8" title="Special:BookSources/978-981-4289-65-8"><bdi>978-981-4289-65-8</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Game+Theory%3A+A+Nontechnical+Introduction+to+the+Analysis+of+Strategy&rft.pub=World+Scientific&rft.date=2010&rft.isbn=978-981-4289-65-8&rft.aulast=McCain&rft.aufirst=Roger+A.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGame+theory" class="Z3988"></span></li></ul> <div class="mw-heading mw-heading3"><h3 id="Historically_important_texts">Historically important texts</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Game_theory&action=edit&section=51" title="Edit section: Historically important texts"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFAumannShapley1974" class="citation cs2"><a href="/wiki/Robert_Aumann" title="Robert Aumann">Aumann, R. J.</a>; <a href="/wiki/Lloyd_Shapley" title="Lloyd Shapley">Shapley, L. S.</a> (1974), <i>Values of Non-Atomic Games</i>, Princeton University Press</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Values+of+Non-Atomic+Games&rft.pub=Princeton+University+Press&rft.date=1974&rft.aulast=Aumann&rft.aufirst=R.+J.&rft.au=Shapley%2C+L.+S.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGame+theory" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFCournot1838" class="citation cs2"><a href="/wiki/Antoine_Augustin_Cournot" title="Antoine Augustin Cournot">Cournot, A. Augustin</a> (1838), "Recherches sur les principles mathematiques de la théorie des richesses", <i>Libraire des Sciences Politiques et Sociales</i></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Libraire+des+Sciences+Politiques+et+Sociales&rft.atitle=Recherches+sur+les+principles+mathematiques+de+la+th%C3%A9orie+des+richesses&rft.date=1838&rft.aulast=Cournot&rft.aufirst=A.+Augustin&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGame+theory" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFEdgeworth1881" class="citation cs2"><a href="/wiki/Francis_Ysidro_Edgeworth" title="Francis Ysidro Edgeworth">Edgeworth, Francis Y.</a> (1881), <a rel="nofollow" class="external text" href="https://books.google.com/books?id=CElYAAAAcAAJ"><i>Mathematical Psychics</i></a>, London: Kegan Paul</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Mathematical+Psychics&rft.place=London&rft.pub=Kegan+Paul&rft.date=1881&rft.aulast=Edgeworth&rft.aufirst=Francis+Y.&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DCElYAAAAcAAJ&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGame+theory" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFFarquharson1969" class="citation cs2"><a href="/wiki/Robin_Farquharson" title="Robin Farquharson">Farquharson, Robin</a> (1969), <i>Theory of Voting</i>, Blackwell (Yale U.P. in the U.S.), <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-631-12460-3" title="Special:BookSources/978-0-631-12460-3"><bdi>978-0-631-12460-3</bdi></a></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Theory+of+Voting&rft.pub=Blackwell+%28Yale+U.P.+in+the+U.S.%29&rft.date=1969&rft.isbn=978-0-631-12460-3&rft.aulast=Farquharson&rft.aufirst=Robin&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGame+theory" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFLuceRaiffa1957" class="citation cs2"><a href="/wiki/R._Duncan_Luce" title="R. Duncan Luce">Luce, R. Duncan</a>; <a href="/wiki/Howard_Raiffa" title="Howard Raiffa">Raiffa, Howard</a> (1957), <i>Games and decisions: introduction and critical survey</i>, New York: <a href="/wiki/John_Wiley_%26_Sons" class="mw-redirect" title="John Wiley & Sons">Wiley</a></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Games+and+decisions%3A+introduction+and+critical+survey&rft.place=New+York&rft.pub=Wiley&rft.date=1957&rft.aulast=Luce&rft.aufirst=R.+Duncan&rft.au=Raiffa%2C+Howard&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGame+theory" class="Z3988"></span></li></ul> <dl><dd><ul><li>reprinted edition: <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFR._Duncan_LuceHoward_Raiffa1989" class="citation cs2">R. Duncan Luce; Howard Raiffa (1989), <i>Games and decisions: introduction and critical survey</i>, New York: <a href="/wiki/Dover_Publications" title="Dover Publications">Dover Publications</a>, <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-486-65943-5" title="Special:BookSources/978-0-486-65943-5"><bdi>978-0-486-65943-5</bdi></a></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Games+and+decisions%3A+introduction+and+critical+survey&rft.place=New+York&rft.pub=Dover+Publications&rft.date=1989&rft.isbn=978-0-486-65943-5&rft.au=R.+Duncan+Luce&rft.au=Howard+Raiffa&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGame+theory" class="Z3988"></span></li></ul></dd></dl> <ul><li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFMaynard_Smith1982" class="citation cs2"><a href="/wiki/John_Maynard_Smith" title="John Maynard Smith">Maynard Smith, John</a> (1982), <a href="/wiki/Evolution_and_the_Theory_of_Games" title="Evolution and the Theory of Games"><i>Evolution and the theory of games</i></a>, Cambridge University Press, <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-521-28884-2" title="Special:BookSources/978-0-521-28884-2"><bdi>978-0-521-28884-2</bdi></a></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Evolution+and+the+theory+of+games&rft.pub=Cambridge+University+Press&rft.date=1982&rft.isbn=978-0-521-28884-2&rft.aulast=Maynard+Smith&rft.aufirst=John&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGame+theory" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFNash1950" class="citation cs2"><a href="/wiki/John_Forbes_Nash" class="mw-redirect" title="John Forbes Nash">Nash, John</a> (1950), "Equilibrium points in n-person games", <i>Proceedings of the National Academy of Sciences of the United States of America</i>, <b>36</b> (1): 48–49, <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1950PNAS...36...48N">1950PNAS...36...48N</a>, <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://doi.org/10.1073%2Fpnas.36.1.48">10.1073/pnas.36.1.48</a></span>, <a href="/wiki/PMC_(identifier)" class="mw-redirect" title="PMC (identifier)">PMC</a> <span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://www.ncbi.nlm.nih.gov/pmc/articles/PMC1063129">1063129</a></span>, <a href="/wiki/PMID_(identifier)" class="mw-redirect" title="PMID (identifier)">PMID</a> <a rel="nofollow" class="external text" href="https://pubmed.ncbi.nlm.nih.gov/16588946">16588946</a></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Proceedings+of+the+National+Academy+of+Sciences+of+the+United+States+of+America&rft.atitle=Equilibrium+points+in+n-person+games&rft.volume=36&rft.issue=1&rft.pages=48-49&rft.date=1950&rft_id=https%3A%2F%2Fwww.ncbi.nlm.nih.gov%2Fpmc%2Farticles%2FPMC1063129%23id-name%3DPMC&rft_id=info%3Apmid%2F16588946&rft_id=info%3Adoi%2F10.1073%2Fpnas.36.1.48&rft_id=info%3Abibcode%2F1950PNAS...36...48N&rft.aulast=Nash&rft.aufirst=John&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGame+theory" class="Z3988"></span></li> <li><a href="/wiki/Lloyd_Shapley" title="Lloyd Shapley">Shapley, L.S.</a> (1953), A Value for n-person Games, In: Contributions to the Theory of Games volume II, H. W. Kuhn and A. W. Tucker (eds.)</li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFShapley1953" class="citation journal cs1"><a href="/wiki/Lloyd_Shapley" title="Lloyd Shapley">Shapley, L. S.</a> (October 1953). <a rel="nofollow" class="external text" href="https://www.ncbi.nlm.nih.gov/pmc/articles/PMC1063912">"Stochastic Games"</a>. <i>Proceedings of the National Academy of Sciences</i>. <b>39</b> (10): 1095–1100. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1953PNAS...39.1095S">1953PNAS...39.1095S</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://doi.org/10.1073%2Fpnas.39.10.1095">10.1073/pnas.39.10.1095</a></span>. <a href="/wiki/PMC_(identifier)" class="mw-redirect" title="PMC (identifier)">PMC</a> <span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://www.ncbi.nlm.nih.gov/pmc/articles/PMC1063912">1063912</a></span>. <a href="/wiki/PMID_(identifier)" class="mw-redirect" title="PMID (identifier)">PMID</a> <a rel="nofollow" class="external text" href="https://pubmed.ncbi.nlm.nih.gov/16589380">16589380</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Proceedings+of+the+National+Academy+of+Sciences&rft.atitle=Stochastic+Games&rft.volume=39&rft.issue=10&rft.pages=1095-1100&rft.date=1953-10&rft_id=https%3A%2F%2Fwww.ncbi.nlm.nih.gov%2Fpmc%2Farticles%2FPMC1063912%23id-name%3DPMC&rft_id=info%3Apmid%2F16589380&rft_id=info%3Adoi%2F10.1073%2Fpnas.39.10.1095&rft_id=info%3Abibcode%2F1953PNAS...39.1095S&rft.aulast=Shapley&rft.aufirst=L.+S.&rft_id=https%3A%2F%2Fwww.ncbi.nlm.nih.gov%2Fpmc%2Farticles%2FPMC1063912&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGame+theory" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFvon_Neumann1928" class="citation cs2">von Neumann, John (1928), "Zur Theorie der Gesellschaftsspiele", <i><a href="/wiki/Mathematische_Annalen" title="Mathematische Annalen">Mathematische Annalen</a></i>, <b>100</b> (1): 295–320, <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1007%2Fbf01448847">10.1007/bf01448847</a>, <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:122961988">122961988</a></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Mathematische+Annalen&rft.atitle=Zur+Theorie+der+Gesellschaftsspiele&rft.volume=100&rft.issue=1&rft.pages=295-320&rft.date=1928&rft_id=info%3Adoi%2F10.1007%2Fbf01448847&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A122961988%23id-name%3DS2CID&rft.aulast=von+Neumann&rft.aufirst=John&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGame+theory" class="Z3988"></span> English translation: "On the Theory of Games of Strategy," in A. W. Tucker and R. D. Luce, ed. (1959), <i>Contributions to the Theory of Games</i>, v. 4, p. <a rel="nofollow" class="external text" href="https://books.google.com/books?id=9lSVFzsTGWsC&pg=PA42">42.</a> Princeton University Press.</li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFvon_NeumannMorgenstern1944" class="citation cs2"><a href="/wiki/John_von_Neumann" title="John von Neumann">von Neumann, John</a>; <a href="/wiki/Oskar_Morgenstern" title="Oskar Morgenstern">Morgenstern, Oskar</a> (1944), <a href="/wiki/Theory_of_games_and_economic_behavior" class="mw-redirect" title="Theory of games and economic behavior">"Theory of games and economic behavior"</a>, <i>Nature</i>, <b>157</b> (3981), Princeton University Press: 172, <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1946Natur.157..172R">1946Natur.157..172R</a>, <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1038%2F157172a0">10.1038/157172a0</a>, <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:29754824">29754824</a></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Nature&rft.atitle=Theory+of+games+and+economic+behavior&rft.volume=157&rft.issue=3981&rft.pages=172&rft.date=1944&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A29754824%23id-name%3DS2CID&rft_id=info%3Adoi%2F10.1038%2F157172a0&rft_id=info%3Abibcode%2F1946Natur.157..172R&rft.aulast=von+Neumann&rft.aufirst=John&rft.au=Morgenstern%2C+Oskar&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGame+theory" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFZermelo1913" class="citation cs2"><a href="/wiki/Ernst_Zermelo" title="Ernst Zermelo">Zermelo, Ernst</a> (1913), "Über eine Anwendung der Mengenlehre auf die Theorie des Schachspiels", <i>Proceedings of the Fifth International Congress of Mathematicians</i>, <b>2</b>: 501–4</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Proceedings+of+the+Fifth+International+Congress+of+Mathematicians&rft.atitle=%C3%9Cber+eine+Anwendung+der+Mengenlehre+auf+die+Theorie+des+Schachspiels&rft.volume=2&rft.pages=501-4&rft.date=1913&rft.aulast=Zermelo&rft.aufirst=Ernst&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGame+theory" class="Z3988"></span></li></ul> <div class="mw-heading mw-heading3"><h3 id="Other_material">Other material</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Game_theory&action=edit&section=52" title="Edit section: Other material"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/Allan_Gibbard" title="Allan Gibbard">Allan Gibbard</a>, "Manipulation of voting schemes: a general result", <i>Econometrica</i>, Vol. 41, No. 4 (1973), pp. 587–601.</li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFMcDonald1950–1996" class="citation cs2">McDonald, John (1950–1996), <i>Strategy in Poker, Business & War</i>, <a href="/wiki/W._W._Norton" class="mw-redirect" title="W. W. Norton">W. W. Norton</a>, <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-393-31457-1" title="Special:BookSources/978-0-393-31457-1"><bdi>978-0-393-31457-1</bdi></a></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Strategy+in+Poker%2C+Business+%26+War&rft.pub=W.+W.+Norton&rft.date=1950%2F1996&rft.isbn=978-0-393-31457-1&rft.aulast=McDonald&rft.aufirst=John&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGame+theory" class="Z3988"></span>. A layman's introduction.</li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFPapayoanou2010" class="citation cs2">Papayoanou, Paul (2010), <i>Game Theory for Business: A Primer in Strategic Gaming</i>, <a href="/wiki/Probabilistic" class="mw-redirect" title="Probabilistic">Probabilistic</a>, <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-9647938-7-3" title="Special:BookSources/978-0-9647938-7-3"><bdi>978-0-9647938-7-3</bdi></a></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Game+Theory+for+Business%3A+A+Primer+in+Strategic+Gaming&rft.pub=Probabilistic&rft.date=2010&rft.isbn=978-0-9647938-7-3&rft.aulast=Papayoanou&rft.aufirst=Paul&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGame+theory" class="Z3988"></span>.</li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFSatterthwaite1975" class="citation journal cs1">Satterthwaite, Mark Allen (April 1975). <a rel="nofollow" class="external text" href="http://www.kellogg.northwestern.edu/research/math/papers/122.pdf">"Strategy-proofness and Arrow's conditions: Existence and correspondence theorems for voting procedures and social welfare functions"</a> <span class="cs1-format">(PDF)</span>. <i>Journal of Economic Theory</i>. <b>10</b> (2): 187–217. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1016%2F0022-0531%2875%2990050-2">10.1016/0022-0531(75)90050-2</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Journal+of+Economic+Theory&rft.atitle=Strategy-proofness+and+Arrow%27s+conditions%3A+Existence+and+correspondence+theorems+for+voting+procedures+and+social+welfare+functions&rft.volume=10&rft.issue=2&rft.pages=187-217&rft.date=1975-04&rft_id=info%3Adoi%2F10.1016%2F0022-0531%2875%2990050-2&rft.aulast=Satterthwaite&rft.aufirst=Mark+Allen&rft_id=http%3A%2F%2Fwww.kellogg.northwestern.edu%2Fresearch%2Fmath%2Fpapers%2F122.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGame+theory" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFSiegfried2006" class="citation cs2">Siegfried, Tom (2006), <i>A Beautiful Math</i>, Joseph Henry Press, <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-309-10192-9" title="Special:BookSources/978-0-309-10192-9"><bdi>978-0-309-10192-9</bdi></a></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=A+Beautiful+Math&rft.pub=Joseph+Henry+Press&rft.date=2006&rft.isbn=978-0-309-10192-9&rft.aulast=Siegfried&rft.aufirst=Tom&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGame+theory" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFSkyrms1990" class="citation cs2"><a href="/wiki/Brian_Skyrms" title="Brian Skyrms">Skyrms, Brian</a> (1990), <i>The Dynamics of Rational Deliberation</i>, <a href="/wiki/Harvard_University_Press" title="Harvard University Press">Harvard University Press</a>, <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-674-21885-7" title="Special:BookSources/978-0-674-21885-7"><bdi>978-0-674-21885-7</bdi></a></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=The+Dynamics+of+Rational+Deliberation&rft.pub=Harvard+University+Press&rft.date=1990&rft.isbn=978-0-674-21885-7&rft.aulast=Skyrms&rft.aufirst=Brian&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGame+theory" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFThrallLucas1963" class="citation cs2"><a href="/wiki/Robert_M._Thrall" title="Robert M. Thrall">Thrall, Robert M.</a>; Lucas, William F. (1963), "<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle n}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>n</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle n}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a601995d55609f2d9f5e233e36fbe9ea26011b3b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.395ex; height:1.676ex;" alt="{\displaystyle n}"></span>-person games in partition function form", <i>Naval Research Logistics Quarterly</i>, <b>10</b> (4): 281–298, <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1002%2Fnav.3800100126">10.1002/nav.3800100126</a></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Naval+Research+Logistics+Quarterly&rft.atitle=MATH+RENDER+ERROR-person+games+in+partition+function+form&rft.volume=10&rft.issue=4&rft.pages=281-298&rft.date=1963&rft_id=info%3Adoi%2F10.1002%2Fnav.3800100126&rft.aulast=Thrall&rft.aufirst=Robert+M.&rft.au=Lucas%2C+William+F.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGame+theory" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFDolevPanagopoulouRabieSchiller2011" class="citation book cs1">Dolev, Shlomi; Panagopoulou, Panagiota N.; Rabie, Mikaël; Schiller, Elad M.; Spirakis, Paul G. (2011). <a rel="nofollow" class="external text" href="http://publications.lib.chalmers.se/publication/230780-rationality-authority-for-provable-rational-behavior">"Rationality authority for provable rational behavior"</a>. <i>Proceedings of the 30th annual ACM SIGACT-SIGOPS symposium on Principles of distributed computing</i>. pp. 289–290. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1145%2F1993806.1993858">10.1145/1993806.1993858</a>. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-1-4503-0719-2" title="Special:BookSources/978-1-4503-0719-2"><bdi>978-1-4503-0719-2</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=Rationality+authority+for+provable+rational+behavior&rft.btitle=Proceedings+of+the+30th+annual+ACM+SIGACT-SIGOPS+symposium+on+Principles+of+distributed+computing&rft.pages=289-290&rft.date=2011&rft_id=info%3Adoi%2F10.1145%2F1993806.1993858&rft.isbn=978-1-4503-0719-2&rft.aulast=Dolev&rft.aufirst=Shlomi&rft.au=Panagopoulou%2C+Panagiota+N.&rft.au=Rabie%2C+Mika%C3%ABl&rft.au=Schiller%2C+Elad+M.&rft.au=Spirakis%2C+Paul+G.&rft_id=http%3A%2F%2Fpublications.lib.chalmers.se%2Fpublication%2F230780-rationality-authority-for-provable-rational-behavior&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGame+theory" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFChastainLivnatPapadimitriouVazirani2014" class="citation cs2">Chastain, Erick; Livnat, Adi; <a href="/wiki/Christos_Papadimitriou" title="Christos Papadimitriou">Papadimitriou, Christos</a>; <a href="/wiki/Umesh_Vazirani" title="Umesh Vazirani">Vazirani, Umesh</a> (June 2014), "Algorithms, games, and evolution", <i><a href="/wiki/Proceedings_of_the_National_Academy_of_Sciences_of_the_United_States_of_America" title="Proceedings of the National Academy of Sciences of the United States of America">Proceedings of the National Academy of Sciences of the United States of America</a></i>, <b>111</b> (29): 10620–10623, <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2014PNAS..11110620C">2014PNAS..11110620C</a>, <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://doi.org/10.1073%2Fpnas.1406556111">10.1073/pnas.1406556111</a></span>, <a href="/wiki/PMC_(identifier)" class="mw-redirect" title="PMC (identifier)">PMC</a> <span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4115542">4115542</a></span>, <a href="/wiki/PMID_(identifier)" class="mw-redirect" title="PMID (identifier)">PMID</a> <a rel="nofollow" class="external text" href="https://pubmed.ncbi.nlm.nih.gov/24979793">24979793</a></cite><span 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related to <i><b><a href="https://en.wikiquote.org/wiki/Special:Search/Game_theory" class="extiw" title="q:Special:Search/Game theory">Game theory</a></b></i>.</div></div> </div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1235681985"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1237033735"><div class="side-box side-box-right plainlinks sistersitebox"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1126788409"> <div class="side-box-flex"> <div class="side-box-image"><span class="noviewer" typeof="mw:File"><span><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/9/99/Wiktionary-logo-en-v2.svg/40px-Wiktionary-logo-en-v2.svg.png" decoding="async" width="40" height="40" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/9/99/Wiktionary-logo-en-v2.svg/60px-Wiktionary-logo-en-v2.svg.png 1.5x, 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class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/0/0b/Wikiversity_logo_2017.svg/60px-Wikiversity_logo_2017.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/0/0b/Wikiversity_logo_2017.svg/80px-Wikiversity_logo_2017.svg.png 2x" data-file-width="626" data-file-height="512" /></span></span></div> <div class="side-box-text plainlist">Wikiversity has learning resources about <i><b><a href="https://en.wikiversity.org/wiki/Game_Theory" class="extiw" title="v:Game Theory">Game Theory</a></b></i></div></div> </div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1235681985"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1237033735"><div class="side-box side-box-right plainlinks sistersitebox"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1126788409"> <div class="side-box-flex"> <div class="side-box-image"><span class="noviewer" typeof="mw:File"><span><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/d/df/Wikibooks-logo-en-noslogan.svg/40px-Wikibooks-logo-en-noslogan.svg.png" decoding="async" width="40" height="40" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/d/df/Wikibooks-logo-en-noslogan.svg/60px-Wikibooks-logo-en-noslogan.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/d/df/Wikibooks-logo-en-noslogan.svg/80px-Wikibooks-logo-en-noslogan.svg.png 2x" data-file-width="400" data-file-height="400" /></span></span></div> <div class="side-box-text plainlist">Wikibooks has a book on the topic of: <i><b><a href="https://en.wikibooks.org/wiki/Introduction_to_Game_Theory" class="extiw" title="wikibooks:Introduction to Game Theory">Introduction to Game Theory</a></b></i></div></div> </div> <ul><li>James Miller (2015): <a rel="nofollow" class="external text" href="https://www.youtube.com/playlist?list=PLqekkRyYeow3cR9U4c4wkIekm2pXxORPn">Introductory Game Theory Videos</a>.</li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation cs2"><a rel="nofollow" class="external text" href="https://www.encyclopediaofmath.org/index.php?title=Games,_theory_of">"Games, theory of"</a>, <i><a href="/wiki/Encyclopedia_of_Mathematics" title="Encyclopedia of Mathematics">Encyclopedia of Mathematics</a></i>, <a href="/wiki/European_Mathematical_Society" title="European Mathematical Society">EMS Press</a>, 2001 [1994]</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=Games%2C+theory+of&rft.btitle=Encyclopedia+of+Mathematics&rft.pub=EMS+Press&rft.date=2001&rft_id=https%3A%2F%2Fwww.encyclopediaofmath.org%2Findex.php%3Ftitle%3DGames%2C_theory_of&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGame+theory" class="Z3988"></span></li> <li>Paul Walker: <a rel="nofollow" class="external text" href="https://web.archive.org/web/20000815223335/http://www.economics.harvard.edu/~aroth/alroth.html">History of Game Theory Page</a>.</li> <li>David Levine: <a rel="nofollow" class="external text" href="http://dklevine.com/">Game Theory. Papers, Lecture Notes and much more stuff.</a></li> <li>Alvin Roth:<link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://web.archive.org/web/20000815223335/http://www.economics.harvard.edu/~aroth/alroth.html">"Game Theory and Experimental Economics page"</a>. Archived from <a rel="nofollow" class="external text" href="http://www.economics.harvard.edu/~aroth/alroth.html">the original</a> on 15 August 2000<span class="reference-accessdate">. Retrieved <span class="nowrap">13 September</span> 2003</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Game+Theory+and+Experimental+Economics+page&rft_id=http%3A%2F%2Fwww.economics.harvard.edu%2F~aroth%2Falroth.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGame+theory" class="Z3988"></span> — Comprehensive list of links to game theory information on the Web</li> <li>Adam Kalai: <a rel="nofollow" class="external text" href="https://web.archive.org/web/20080416035356/http://wiki.cc.gatech.edu/theory/index.php/CS_8803_-_Game_Theory_and_Computer_Science._Spring_2008">Game Theory and Computer Science</a> — Lecture notes on Game Theory and Computer Science</li> <li>Mike Shor: <a rel="nofollow" class="external text" href="http://www.gametheory.net/">GameTheory.net</a> — Lecture notes, interactive illustrations and other information.</li> <li>Jim Ratliff's <a rel="nofollow" class="external text" href="http://virtualperfection.com/gametheory/">Graduate Course in Game Theory</a> (lecture notes).</li> <li>Don Ross: <a rel="nofollow" class="external text" href="http://plato.stanford.edu/entries/game-theory/">Review Of Game Theory</a> in the <i>Stanford Encyclopedia of Philosophy</i>.</li> <li>Bruno Verbeek and Christopher Morris: <a rel="nofollow" class="external text" href="http://plato.stanford.edu/entries/game-ethics/">Game Theory and Ethics</a></li> <li>Elmer G. Wiens: <a rel="nofollow" class="external text" href="http://www.egwald.ca/operationsresearch/gameintroduction.php">Game Theory</a> — Introduction, worked examples, play online two-person zero-sum games.</li> <li>Marek M. Kaminski: <a rel="nofollow" class="external text" href="http://webfiles.uci.edu/mkaminsk/www/courses.html">Game Theory and Politics</a> <a rel="nofollow" class="external text" href="https://web.archive.org/web/20061020072523/http://webfiles.uci.edu/mkaminsk/www/courses.html">Archived</a> 20 October 2006 at the <a href="/wiki/Wayback_Machine" title="Wayback Machine">Wayback Machine</a> — Syllabuses and lecture notes for game theory and political science.</li> <li><a rel="nofollow" class="external text" href="http://www.socialcapitalgateway.org/eng-gametheory.htm">Websites on game theory and social interactions</a></li> <li>Kesten Green's <a rel="nofollow" class="external text" href="https://web.archive.org/web/20110411143752/http://conflictforecasting.com/">Conflict Forecasting</a> at the <a href="/wiki/Wayback_Machine" title="Wayback Machine">Wayback Machine</a> (archived 11 April 2011) — See <a rel="nofollow" class="external text" href="http://www.forecastingprinciples.com/paperpdf/Greenforecastinginconflict.pdf">Papers</a> for <a rel="nofollow" class="external text" href="http://www.decisionworkshops.com/#/graphs-of-findings/4553562008">evidence on the accuracy of forecasts from game theory and other methods</a> <a rel="nofollow" class="external text" href="https://web.archive.org/web/20190915052113/http://www.decisionworkshops.com/#/graphs-of-findings/4553562008">Archived</a> 15 September 2019 at the <a href="/wiki/Wayback_Machine" title="Wayback Machine">Wayback Machine</a>.</li> <li>McKelvey, Richard D., McLennan, Andrew M., and Turocy, Theodore L. (2007) <i><a rel="nofollow" class="external text" href="http://gambit.sourceforge.net/">Gambit: Software Tools for Game Theory</a></i>.</li> <li>Benjamin Polak: <a rel="nofollow" class="external text" href="http://oyc.yale.edu/economics/game-theory">Open Course on Game Theory at Yale</a> <a rel="nofollow" class="external text" href="https://web.archive.org/web/20100803224320/http://oyc.yale.edu/economics/game-theory">Archived</a> 3 August 2010 at the <a href="/wiki/Wayback_Machine" title="Wayback Machine">Wayback Machine</a> <a rel="nofollow" class="external text" href="https://www.youtube.com/playlist?list=PL6EF60E1027E1A10B">videos of the course</a></li> <li>Benjamin Moritz, Bernhard Könsgen, Danny Bures, Ronni Wiersch, (2007) <i><a rel="nofollow" class="external text" href="https://web.archive.org/web/20130718133141/http://www.spieltheorie-software.de/">Spieltheorie-Software.de: An application for Game Theory implemented in JAVA</a></i>.</li> <li>Antonin Kucera: <a rel="nofollow" class="external text" href="http://slideslive.com/38891162/stochastic-twoplayer-games">Stochastic Two-Player Games</a>.</li> <li>Yu-Chi Ho: <a rel="nofollow" class="external text" href="http://blog.sciencenet.cn/home.php?mod=space&uid=1565&do=blog&id=17894">What is Mathematical Game Theory</a>; <a rel="nofollow" class="external text" href="http://blog.sciencenet.cn/home.php?mod=space&uid=1565&do=blog&id=20337">What is Mathematical Game Theory (#2)</a>; <a rel="nofollow" class="external text" href="http://blog.sciencenet.cn/home.php?mod=space&uid=1565&do=blog&id=21210">What is Mathematical Game Theory (#3)</a>; <a rel="nofollow" class="external text" href="http://blog.sciencenet.cn/home.php?mod=space&uid=1565&do=blog&id=21735">What is Mathematical Game Theory (#4)-Many person game theory</a>; <a rel="nofollow" class="external text" href="http://blog.sciencenet.cn/home.php?mod=space&uid=1565&do=blog&id=21891">What is Mathematical Game Theory ?( #5) – Finale, summing up, and my own view</a></li></ul> <p class="mw-empty-elt"> </p> <div class="navbox-styles"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><style data-mw-deduplicate="TemplateStyles:r1236075235">.mw-parser-output .navbox{box-sizing:border-box;border:1px solid #a2a9b1;width:100%;clear:both;font-size:88%;text-align:center;padding:1px;margin:1em auto 0}.mw-parser-output .navbox .navbox{margin-top:0}.mw-parser-output .navbox+.navbox,.mw-parser-output .navbox+.navbox-styles+.navbox{margin-top:-1px}.mw-parser-output .navbox-inner,.mw-parser-output .navbox-subgroup{width:100%}.mw-parser-output .navbox-group,.mw-parser-output .navbox-title,.mw-parser-output .navbox-abovebelow{padding:0.25em 1em;line-height:1.5em;text-align:center}.mw-parser-output .navbox-group{white-space:nowrap;text-align:right}.mw-parser-output .navbox,.mw-parser-output .navbox-subgroup{background-color:#fdfdfd}.mw-parser-output .navbox-list{line-height:1.5em;border-color:#fdfdfd}.mw-parser-output .navbox-list-with-group{text-align:left;border-left-width:2px;border-left-style:solid}.mw-parser-output tr+tr>.navbox-abovebelow,.mw-parser-output tr+tr>.navbox-group,.mw-parser-output tr+tr>.navbox-image,.mw-parser-output tr+tr>.navbox-list{border-top:2px solid #fdfdfd}.mw-parser-output .navbox-title{background-color:#ccf}.mw-parser-output .navbox-abovebelow,.mw-parser-output .navbox-group,.mw-parser-output .navbox-subgroup .navbox-title{background-color:#ddf}.mw-parser-output .navbox-subgroup .navbox-group,.mw-parser-output .navbox-subgroup .navbox-abovebelow{background-color:#e6e6ff}.mw-parser-output .navbox-even{background-color:#f7f7f7}.mw-parser-output .navbox-odd{background-color:transparent}.mw-parser-output .navbox .hlist td dl,.mw-parser-output .navbox .hlist td ol,.mw-parser-output .navbox .hlist td ul,.mw-parser-output .navbox td.hlist dl,.mw-parser-output .navbox td.hlist ol,.mw-parser-output .navbox td.hlist ul{padding:0.125em 0}.mw-parser-output .navbox .navbar{display:block;font-size:100%}.mw-parser-output .navbox-title .navbar{float:left;text-align:left;margin-right:0.5em}body.skin--responsive .mw-parser-output .navbox-image img{max-width:none!important}@media print{body.ns-0 .mw-parser-output .navbox{display:none!important}}</style></div><div role="navigation" class="navbox" aria-labelledby="Topics_of_game_theory" style="padding:3px"><table class="nowraplinks mw-collapsible autocollapse navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1239400231"><div class="navbar plainlinks hlist navbar-mini"><ul><li class="nv-view"><a href="/wiki/Template:Game_theory" title="Template:Game theory"><abbr title="View this template">v</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:Game_theory" title="Template talk:Game theory"><abbr title="Discuss this template">t</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:EditPage/Template:Game_theory" title="Special:EditPage/Template:Game theory"><abbr title="Edit this template">e</abbr></a></li></ul></div><div id="Topics_of_game_theory" style="font-size:114%;margin:0 4em">Topics of <a class="mw-selflink selflink">game theory</a></div></th></tr><tr><th scope="row" class="navbox-group" style="width:1%">Definitions</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Congestion_game" title="Congestion game">Congestion game</a></li> <li><a href="/wiki/Cooperative_game_theory" title="Cooperative game theory">Cooperative game</a></li> <li><a href="/wiki/Determinacy" title="Determinacy">Determinacy</a></li> <li><a href="/wiki/Escalation_of_commitment" title="Escalation of commitment">Escalation of commitment</a></li> <li><a href="/wiki/Extensive-form_game" title="Extensive-form game">Extensive-form game</a></li> <li><a href="/wiki/First-player_and_second-player_win" title="First-player and second-player win">First-player and second-player win</a></li> <li><a href="/wiki/Game_complexity" title="Game complexity">Game complexity</a></li> <li><a href="/wiki/Graphical_game_theory" title="Graphical game theory">Graphical game</a></li> <li><a href="/wiki/Hierarchy_of_beliefs" title="Hierarchy of beliefs">Hierarchy of beliefs</a></li> <li><a href="/wiki/Information_set_(game_theory)" title="Information set (game theory)">Information set</a></li> <li><a href="/wiki/Normal-form_game" title="Normal-form game">Normal-form game</a></li> <li><a href="/wiki/Preference_(economics)" title="Preference (economics)">Preference</a></li> <li><a href="/wiki/Sequential_game" title="Sequential game">Sequential game</a></li> <li><a href="/wiki/Simultaneous_game" title="Simultaneous game">Simultaneous game</a></li> <li><a href="/wiki/Simultaneous_action_selection" title="Simultaneous action selection">Simultaneous action selection</a></li> <li><a href="/wiki/Solved_game" title="Solved game">Solved game</a></li> <li><a href="/wiki/Succinct_game" title="Succinct game">Succinct game</a></li> <li><a href="/wiki/Mechanism_design" title="Mechanism design">Mechanism design</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Economic_equilibrium" title="Economic equilibrium">Equilibrium</a><br /><a href="/wiki/Solution_concept" title="Solution concept">concepts</a></th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Bayes_correlated_equilibrium" title="Bayes correlated equilibrium">Bayes correlated equilibrium</a></li> <li><a href="/wiki/Bayesian_Nash_equilibrium" class="mw-redirect" title="Bayesian Nash equilibrium">Bayesian Nash equilibrium</a></li> <li><a href="/wiki/Berge_equilibrium" title="Berge equilibrium">Berge equilibrium</a></li> <li><a href="/wiki/Core_(game_theory)" title="Core (game theory)"> Core</a></li> <li><a href="/wiki/Correlated_equilibrium" title="Correlated equilibrium">Correlated equilibrium</a></li> <li><a href="/wiki/Coalition-proof_Nash_equilibrium" title="Coalition-proof Nash equilibrium">Coalition-proof Nash equilibrium</a></li> <li><a href="/wiki/Epsilon-equilibrium" title="Epsilon-equilibrium">Epsilon-equilibrium</a></li> <li><a href="/wiki/Evolutionarily_stable_strategy" title="Evolutionarily stable strategy">Evolutionarily stable strategy</a></li> <li><a href="/wiki/Gibbs_measure" title="Gibbs measure">Gibbs equilibrium</a></li> <li><a href="/wiki/Mertens-stable_equilibrium" title="Mertens-stable equilibrium">Mertens-stable equilibrium</a></li> <li><a href="/wiki/Markov_perfect_equilibrium" title="Markov perfect equilibrium">Markov perfect equilibrium</a></li> <li><a href="/wiki/Nash_equilibrium" title="Nash equilibrium">Nash equilibrium</a></li> <li><a href="/wiki/Pareto_efficiency" title="Pareto efficiency">Pareto efficiency</a></li> <li><a href="/wiki/Perfect_Bayesian_equilibrium" title="Perfect Bayesian equilibrium">Perfect Bayesian equilibrium</a></li> <li><a href="/wiki/Proper_equilibrium" title="Proper equilibrium">Proper equilibrium</a></li> <li><a href="/wiki/Quantal_response_equilibrium" title="Quantal response equilibrium">Quantal response equilibrium</a></li> <li><a href="/wiki/Quasi-perfect_equilibrium" title="Quasi-perfect equilibrium">Quasi-perfect equilibrium</a></li> <li><a href="/wiki/Risk_dominance" title="Risk dominance">Risk dominance</a></li> <li><a href="/wiki/Satisfaction_equilibrium" title="Satisfaction equilibrium">Satisfaction equilibrium</a></li> <li><a href="/wiki/Self-confirming_equilibrium" title="Self-confirming equilibrium">Self-confirming equilibrium</a></li> <li><a href="/wiki/Sequential_equilibrium" title="Sequential equilibrium">Sequential equilibrium</a></li> <li><a href="/wiki/Shapley_value" title="Shapley value">Shapley value</a></li> <li><a href="/wiki/Strong_Nash_equilibrium" title="Strong Nash equilibrium">Strong Nash equilibrium</a></li> <li><a href="/wiki/Subgame_perfect_equilibrium" title="Subgame perfect equilibrium">Subgame perfection</a></li> <li><a href="/wiki/Trembling_hand_perfect_equilibrium" title="Trembling hand perfect equilibrium">Trembling hand equilibrium</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Strategy_(game_theory)" title="Strategy (game theory)">Strategies</a></th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Appeasement" title="Appeasement">Appeasement</a></li> <li><a href="/wiki/Backward_induction" title="Backward induction">Backward induction</a></li> <li><a href="/wiki/Bid_shading" title="Bid shading">Bid shading</a></li> <li><a href="/wiki/Collusion" title="Collusion">Collusion</a></li> <li><a href="/wiki/Cheap_talk" title="Cheap talk">Cheap talk</a></li> <li><a href="/wiki/De-escalation" title="De-escalation">De-escalation</a></li> <li><a href="/wiki/Deterrence_theory" title="Deterrence theory">Deterrence</a></li> <li><a href="/wiki/Conflict_escalation" title="Conflict escalation">Escalation</a></li> <li><a href="/wiki/Forward_induction" class="mw-redirect" title="Forward induction">Forward induction</a></li> <li><a href="/wiki/Grim_trigger" title="Grim trigger">Grim trigger</a></li> <li><a href="/wiki/Markov_strategy" title="Markov strategy">Markov strategy</a></li> <li><a href="/wiki/Pairing_strategy" title="Pairing strategy">Pairing strategy</a></li> <li><a href="/wiki/Strategic_dominance" title="Strategic dominance">Dominant strategies</a></li> <li><a href="/wiki/Strategy_(game_theory)" title="Strategy (game theory)">Pure strategy</a></li> <li><a href="/wiki/Strategy_(game_theory)#Mixed_strategy" title="Strategy (game theory)">Mixed strategy</a></li> <li><a href="/wiki/Strategy-stealing_argument" title="Strategy-stealing argument">Strategy-stealing argument</a></li> <li><a href="/wiki/Tit_for_tat" title="Tit for tat">Tit for tat</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Category:Game_theory_game_classes" title="Category:Game theory game classes">Classes<br />of games</a></th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Auction" title="Auction">Auction</a></li> <li><a href="/wiki/Bargaining_problem" class="mw-redirect" title="Bargaining problem">Bargaining problem</a></li> <li><a href="/wiki/Global_game" title="Global game">Global game</a></li> <li><a href="/wiki/Intransitive_game" title="Intransitive game">Intransitive game</a></li> <li><a href="/wiki/Mean-field_game_theory" title="Mean-field game theory">Mean-field game</a></li> <li><a href="/wiki/N-player_game" title="N-player game"><i>n</i>-player game</a></li> <li><a href="/wiki/Perfect_information" title="Perfect information">Perfect information</a></li> <li><a href="/wiki/Poisson_games" class="mw-redirect" title="Poisson games">Large Poisson game</a></li> <li><a href="/wiki/Potential_game" title="Potential game">Potential game</a></li> <li><a href="/wiki/Repeated_game" title="Repeated game">Repeated game</a></li> <li><a href="/wiki/Screening_game" title="Screening game">Screening game</a></li> <li><a href="/wiki/Signaling_game" title="Signaling game">Signaling game</a></li> <li><a href="/wiki/Strictly_determined_game" title="Strictly determined game">Strictly determined game</a></li> <li><a href="/wiki/Stochastic_game" title="Stochastic game">Stochastic game</a></li> <li><a href="/wiki/Symmetric_game" title="Symmetric game">Symmetric game</a></li> <li><a href="/wiki/Zero-sum_game" title="Zero-sum game">Zero-sum game</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/List_of_games_in_game_theory" title="List of games in game theory">Games</a></th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Go_(game)" title="Go (game)">Go</a></li> <li><a href="/wiki/Chess" title="Chess">Chess</a></li> <li><a href="/wiki/Infinite_chess" title="Infinite chess">Infinite chess</a></li> <li><a href="/wiki/Draughts" class="mw-redirect" title="Draughts">Checkers</a></li> <li><a href="/wiki/All-pay_auction" title="All-pay auction">All-pay auction</a></li> <li><a href="/wiki/Prisoner%27s_dilemma" title="Prisoner's dilemma">Prisoner's dilemma</a></li> <li><a href="/wiki/Gift-exchange_game" title="Gift-exchange game">Gift-exchange game</a></li> <li><a href="/wiki/Optional_prisoner%27s_dilemma" title="Optional prisoner's dilemma">Optional prisoner's dilemma</a></li> <li><a href="/wiki/Traveler%27s_dilemma" title="Traveler's dilemma">Traveler's dilemma</a></li> <li><a href="/wiki/Coordination_game" title="Coordination game">Coordination game</a></li> <li><a href="/wiki/Chicken_(game)" title="Chicken (game)">Chicken</a></li> <li><a href="/wiki/Centipede_game" title="Centipede game">Centipede game</a></li> <li><a href="/wiki/Lewis_signaling_game" title="Lewis signaling game">Lewis signaling game</a></li> <li><a href="/wiki/Volunteer%27s_dilemma" title="Volunteer's dilemma">Volunteer's dilemma</a></li> <li><a href="/wiki/Dollar_auction" title="Dollar auction">Dollar auction</a></li> <li><a href="/wiki/Battle_of_the_sexes_(game_theory)" title="Battle of the sexes (game theory)">Battle of the sexes</a></li> <li><a href="/wiki/Stag_hunt" title="Stag hunt">Stag hunt</a></li> <li><a href="/wiki/Matching_pennies" title="Matching pennies">Matching pennies</a></li> <li><a href="/wiki/Ultimatum_game" title="Ultimatum game">Ultimatum game</a></li> <li><a href="/wiki/Electronic_mail_game" title="Electronic mail game">Electronic mail game</a></li> <li><a href="/wiki/Rock_paper_scissors" title="Rock paper scissors">Rock paper scissors</a></li> <li><a href="/wiki/Pirate_game" title="Pirate game">Pirate game</a></li> <li><a href="/wiki/Dictator_game" title="Dictator game">Dictator game</a></li> <li><a href="/wiki/Public_goods_game" title="Public goods game">Public goods game</a></li> <li><a href="/wiki/Blotto_game" title="Blotto game">Blotto game</a></li> <li><a href="/wiki/War_of_attrition_(game)" title="War of attrition (game)">War of attrition</a></li> <li><a href="/wiki/El_Farol_Bar_problem" title="El Farol Bar problem">El Farol Bar problem</a></li> <li><a href="/wiki/Fair_division" title="Fair division">Fair division</a></li> <li><a href="/wiki/Fair_cake-cutting" title="Fair cake-cutting">Fair cake-cutting</a></li> <li><a href="/wiki/Bertrand_competition" title="Bertrand competition">Bertrand competition</a></li> <li><a href="/wiki/Cournot_competition" title="Cournot competition">Cournot competition</a></li> <li><a href="/wiki/Stackelberg_competition" title="Stackelberg competition">Stackelberg competition</a></li> <li><a href="/wiki/Deadlock_(game_theory)" title="Deadlock (game theory)">Deadlock</a></li> <li><a href="/wiki/Unscrupulous_diner%27s_dilemma" title="Unscrupulous diner's dilemma">Diner's dilemma</a></li> <li><a href="/wiki/Guess_2/3_of_the_average" title="Guess 2/3 of the average">Guess 2/3 of the average</a></li> <li><a href="/wiki/Kuhn_poker" title="Kuhn poker">Kuhn poker</a></li> <li><a href="/wiki/Bargaining_problem" class="mw-redirect" title="Bargaining problem">Nash bargaining game</a></li> <li><a href="/wiki/Induction_puzzles" title="Induction puzzles">Induction puzzles</a></li> <li><a href="/wiki/Dictator_game#Trust_game" title="Dictator game">Trust game</a></li> <li><a href="/wiki/Princess_and_monster_game" title="Princess and monster game">Princess and monster game</a></li> <li><a href="/wiki/Rendezvous_problem" title="Rendezvous problem">Rendezvous problem</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Theorems</th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Aumann%27s_agreement_theorem" title="Aumann's agreement theorem">Aumann's agreement theorem</a></li> <li><a href="/wiki/Folk_theorem_(game_theory)" title="Folk theorem (game theory)">Folk theorem</a></li> <li><a href="/wiki/Minimax" title="Minimax">Minimax theorem</a></li> <li><a href="/wiki/Nash_equilibrium" title="Nash equilibrium">Nash's theorem</a></li> <li><a href="/wiki/Negamax" title="Negamax">Negamax theorem</a></li> <li><a href="/wiki/Purification_theorem" title="Purification theorem">Purification theorem</a></li> <li><a href="/wiki/Revelation_principle" title="Revelation principle">Revelation principle</a></li> <li><a href="/wiki/Sprague%E2%80%93Grundy_theorem" title="Sprague–Grundy theorem">Sprague–Grundy theorem</a></li> <li><a href="/wiki/Zermelo%27s_theorem_(game_theory)" title="Zermelo's theorem (game theory)">Zermelo's theorem</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Key<br />figures</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Albert_W._Tucker" title="Albert W. Tucker">Albert W. Tucker</a></li> <li><a href="/wiki/Amos_Tversky" title="Amos Tversky">Amos Tversky</a></li> <li><a href="/wiki/Antoine_Augustin_Cournot" title="Antoine Augustin Cournot">Antoine Augustin Cournot</a></li> <li><a href="/wiki/Ariel_Rubinstein" title="Ariel Rubinstein">Ariel Rubinstein</a></li> <li><a href="/wiki/Claude_Shannon" title="Claude Shannon">Claude Shannon</a></li> <li><a href="/wiki/Daniel_Kahneman" title="Daniel Kahneman">Daniel Kahneman</a></li> <li><a href="/wiki/David_K._Levine" title="David K. Levine">David K. Levine</a></li> <li><a href="/wiki/David_M._Kreps" title="David M. Kreps">David M. Kreps</a></li> <li><a href="/wiki/Donald_B._Gillies" title="Donald B. Gillies">Donald B. Gillies</a></li> <li><a href="/wiki/Drew_Fudenberg" title="Drew Fudenberg">Drew Fudenberg</a></li> <li><a href="/wiki/Eric_Maskin" title="Eric Maskin">Eric Maskin</a></li> <li><a href="/wiki/Harold_W._Kuhn" title="Harold W. Kuhn">Harold W. Kuhn</a></li> <li><a href="/wiki/Herbert_A._Simon" title="Herbert A. Simon">Herbert Simon</a></li> <li><a href="/wiki/Herv%C3%A9_Moulin" title="Hervé Moulin">Hervé Moulin</a></li> <li><a href="/wiki/John_Conway" class="mw-redirect" title="John Conway">John Conway</a></li> <li><a href="/wiki/Jean_Tirole" title="Jean Tirole">Jean Tirole</a></li> <li><a href="/wiki/Jean-Fran%C3%A7ois_Mertens" title="Jean-François Mertens">Jean-François Mertens</a></li> <li><a href="/wiki/Jennifer_Tour_Chayes" title="Jennifer Tour Chayes">Jennifer Tour Chayes</a></li> <li><a href="/wiki/John_Harsanyi" title="John Harsanyi">John Harsanyi</a></li> <li><a href="/wiki/John_Maynard_Smith" title="John Maynard Smith">John Maynard Smith</a></li> <li><a href="/wiki/John_Forbes_Nash_Jr." title="John Forbes Nash Jr.">John Nash</a></li> <li><a href="/wiki/John_von_Neumann" title="John von Neumann">John von Neumann</a></li> <li><a href="/wiki/Kenneth_Arrow" title="Kenneth Arrow">Kenneth Arrow</a></li> <li><a href="/wiki/Kenneth_Binmore" title="Kenneth Binmore">Kenneth Binmore</a></li> <li><a href="/wiki/Leonid_Hurwicz" title="Leonid Hurwicz">Leonid Hurwicz</a></li> <li><a href="/wiki/Lloyd_Shapley" title="Lloyd Shapley">Lloyd Shapley</a></li> <li><a href="/wiki/Melvin_Dresher" title="Melvin Dresher">Melvin Dresher</a></li> <li><a href="/wiki/Merrill_M._Flood" title="Merrill M. Flood">Merrill M. Flood</a></li> <li><a href="/wiki/Olga_Bondareva" title="Olga Bondareva">Olga Bondareva</a></li> <li><a href="/wiki/Oskar_Morgenstern" title="Oskar Morgenstern">Oskar Morgenstern</a></li> <li><a href="/wiki/Paul_Milgrom" title="Paul Milgrom">Paul Milgrom</a></li> <li><a href="/wiki/Peyton_Young" title="Peyton Young">Peyton Young</a></li> <li><a href="/wiki/Reinhard_Selten" title="Reinhard Selten">Reinhard Selten</a></li> <li><a href="/wiki/Robert_Axelrod_(political_scientist)" title="Robert Axelrod (political scientist)">Robert Axelrod</a></li> <li><a href="/wiki/Robert_Aumann" title="Robert Aumann">Robert Aumann</a></li> <li><a href="/wiki/Robert_B._Wilson" title="Robert B. Wilson">Robert B. Wilson</a></li> <li><a href="/wiki/Roger_Myerson" title="Roger Myerson">Roger Myerson</a></li> <li><a href="/wiki/Samuel_Bowles_(economist)" title="Samuel Bowles (economist)"> Samuel Bowles</a></li> <li><a href="/wiki/Suzanne_Scotchmer" title="Suzanne Scotchmer">Suzanne Scotchmer</a></li> <li><a href="/wiki/Thomas_Schelling" title="Thomas Schelling">Thomas Schelling</a></li> <li><a href="/wiki/William_Vickrey" title="William Vickrey">William Vickrey</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Search optimizations</th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Alpha%E2%80%93beta_pruning" title="Alpha–beta pruning">Alpha–beta pruning</a></li> <li><a href="/wiki/Aspiration_window" title="Aspiration window">Aspiration window</a></li> <li><a href="/wiki/Principal_variation_search" title="Principal variation search">Principal variation search</a></li> <li><a href="/wiki/Max%5En_algorithm" title="Max^n algorithm">max^n algorithm</a></li> <li><a href="/wiki/Paranoid_algorithm" title="Paranoid algorithm">Paranoid algorithm</a></li> <li><a href="/wiki/Lazy_SMP" title="Lazy SMP">Lazy SMP</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Miscellaneous</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Bounded_rationality" title="Bounded rationality">Bounded rationality</a></li> <li><a href="/wiki/Combinatorial_game_theory" title="Combinatorial game theory">Combinatorial game theory</a></li> <li><a href="/wiki/Confrontation_analysis" title="Confrontation analysis">Confrontation analysis</a></li> <li><a href="/wiki/Coopetition" title="Coopetition">Coopetition</a></li> <li><a href="/wiki/Evolutionary_game_theory" title="Evolutionary game theory">Evolutionary game theory</a></li> <li><a href="/wiki/Glossary_of_game_theory" title="Glossary of game theory">Glossary of game theory</a></li> <li><a href="/wiki/List_of_game_theorists" title="List of game theorists">List of game theorists</a></li> <li><a href="/wiki/List_of_games_in_game_theory" title="List of games in game theory">List of games in game theory</a></li> <li><a href="/wiki/No-win_situation" title="No-win situation">No-win situation</a></li> <li><a href="/wiki/Topological_game" title="Topological game">Topological game</a></li> <li><a href="/wiki/Tragedy_of_the_commons" title="Tragedy of the commons">Tragedy of the commons</a></li></ul> </div></td></tr></tbody></table></div> <div class="navbox-styles"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236075235"></div><div role="navigation" class="navbox" aria-labelledby="Major_mathematics_areas" style="padding:3px"><table class="nowraplinks hlist mw-collapsible autocollapse navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1239400231"><div class="navbar plainlinks hlist navbar-mini"><ul><li class="nv-view"><a href="/wiki/Template:Areas_of_mathematics" title="Template:Areas of mathematics"><abbr title="View this template">v</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:Areas_of_mathematics" title="Template talk:Areas of mathematics"><abbr title="Discuss this template">t</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:EditPage/Template:Areas_of_mathematics" title="Special:EditPage/Template:Areas of mathematics"><abbr title="Edit this template">e</abbr></a></li></ul></div><div id="Major_mathematics_areas" style="font-size:114%;margin:0 4em">Major <a href="/wiki/Mathematics" title="Mathematics">mathematics</a> areas</div></th></tr><tr><td class="navbox-abovebelow" colspan="2"><div> <ul><li><a href="/wiki/History_of_mathematics" title="History of mathematics">History</a> <ul><li><a href="/wiki/Timeline_of_mathematics" title="Timeline of mathematics">Timeline</a></li> <li><a href="/wiki/Future_of_mathematics" title="Future of mathematics">Future</a></li></ul></li> <li><a href="/wiki/Lists_of_mathematics_topics" title="Lists of mathematics topics">Lists</a></li> <li><a href="/wiki/Glossary_of_mathematical_symbols" title="Glossary of mathematical symbols">Glossary</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Foundations_of_mathematics" title="Foundations of mathematics">Foundations</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Category_theory" title="Category theory">Category theory</a></li> <li><a href="/wiki/Information_theory" title="Information theory">Information theory</a></li> <li><a href="/wiki/Mathematical_logic" title="Mathematical logic">Mathematical logic</a></li> <li><a href="/wiki/Philosophy_of_mathematics" title="Philosophy of mathematics">Philosophy of mathematics</a></li> <li><a href="/wiki/Set_theory" title="Set theory">Set theory</a></li> <li><a href="/wiki/Type_theory" title="Type theory">Type theory</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Algebra" title="Algebra">Algebra</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Abstract_algebra" title="Abstract algebra">Abstract</a></li> <li><a href="/wiki/Commutative_algebra" title="Commutative algebra">Commutative</a></li> <li><a href="/wiki/Elementary_algebra" title="Elementary algebra">Elementary</a></li> <li><a href="/wiki/Group_theory" title="Group theory">Group theory</a></li> <li><a href="/wiki/Linear_algebra" title="Linear algebra">Linear</a></li> <li><a href="/wiki/Multilinear_algebra" title="Multilinear algebra">Multilinear</a></li> <li><a href="/wiki/Universal_algebra" title="Universal algebra">Universal</a></li> <li><a href="/wiki/Homological_algebra" title="Homological algebra">Homological</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Mathematical_analysis" title="Mathematical analysis">Analysis</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Calculus" title="Calculus">Calculus</a></li> <li><a href="/wiki/Real_analysis" title="Real analysis">Real analysis</a></li> <li><a href="/wiki/Complex_analysis" title="Complex analysis">Complex analysis</a></li> <li><a href="/wiki/Hypercomplex_analysis" title="Hypercomplex analysis">Hypercomplex analysis</a></li> <li><a href="/wiki/Differential_equation" title="Differential equation">Differential equations</a></li> <li><a href="/wiki/Functional_analysis" title="Functional analysis">Functional analysis</a></li> <li><a href="/wiki/Harmonic_analysis" title="Harmonic analysis">Harmonic analysis</a></li> <li><a href="/wiki/Measure_(mathematics)" title="Measure (mathematics)">Measure theory</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Discrete_mathematics" title="Discrete mathematics">Discrete</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Combinatorics" title="Combinatorics">Combinatorics</a></li> <li><a href="/wiki/Graph_theory" title="Graph theory">Graph theory</a></li> <li><a href="/wiki/Order_theory" title="Order theory">Order theory</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Geometry" title="Geometry">Geometry</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Algebraic_geometry" title="Algebraic geometry">Algebraic</a></li> <li><a href="/wiki/Analytic_geometry" title="Analytic geometry">Analytic</a></li> <li><a href="/wiki/Arithmetic_geometry" title="Arithmetic geometry">Arithmetic</a></li> <li><a href="/wiki/Differential_geometry" title="Differential geometry">Differential</a></li> <li><a href="/wiki/Discrete_geometry" title="Discrete geometry">Discrete</a></li> <li><a href="/wiki/Euclidean_geometry" title="Euclidean geometry">Euclidean</a></li> <li><a href="/wiki/Finite_geometry" title="Finite geometry">Finite</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Number_theory" title="Number theory">Number theory</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Arithmetic" title="Arithmetic">Arithmetic</a></li> <li><a href="/wiki/Algebraic_number_theory" title="Algebraic number theory">Algebraic number theory</a></li> <li><a href="/wiki/Analytic_number_theory" title="Analytic number theory">Analytic number theory</a></li> <li><a href="/wiki/Diophantine_geometry" title="Diophantine geometry">Diophantine geometry</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Topology" title="Topology">Topology</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/General_topology" title="General topology">General</a></li> <li><a href="/wiki/Algebraic_topology" title="Algebraic topology">Algebraic</a></li> <li><a href="/wiki/Differential_topology" title="Differential topology">Differential</a></li> <li><a href="/wiki/Geometric_topology" title="Geometric topology">Geometric</a></li> <li><a href="/wiki/Homotopy_theory" title="Homotopy theory">Homotopy theory</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Applied_mathematics" title="Applied mathematics">Applied</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Engineering_mathematics" title="Engineering mathematics">Engineering mathematics</a></li> <li><a href="/wiki/Mathematical_and_theoretical_biology" title="Mathematical and theoretical biology">Mathematical biology</a></li> <li><a href="/wiki/Mathematical_chemistry" title="Mathematical chemistry">Mathematical chemistry</a></li> <li><a href="/wiki/Mathematical_economics" title="Mathematical economics">Mathematical economics</a></li> <li><a href="/wiki/Mathematical_finance" title="Mathematical finance">Mathematical finance</a></li> <li><a href="/wiki/Mathematical_physics" title="Mathematical physics">Mathematical physics</a></li> <li><a href="/wiki/Mathematical_psychology" title="Mathematical psychology">Mathematical psychology</a></li> <li><a href="/wiki/Mathematical_sociology" title="Mathematical sociology">Mathematical sociology</a></li> <li><a href="/wiki/Mathematical_statistics" title="Mathematical statistics">Mathematical statistics</a></li> <li><a href="/wiki/Probability_theory" title="Probability theory">Probability</a></li> <li><a href="/wiki/Statistics" title="Statistics">Statistics</a></li> <li><a href="/wiki/Systems_science" title="Systems science">Systems science</a> <ul><li><a href="/wiki/Control_theory" title="Control theory">Control theory</a></li> <li><a class="mw-selflink selflink">Game theory</a></li> <li><a href="/wiki/Operations_research" title="Operations research">Operations research</a></li></ul></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Computational_mathematics" title="Computational mathematics">Computational</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Computer_science" title="Computer science">Computer science</a></li> <li><a href="/wiki/Theory_of_computation" title="Theory of computation">Theory of computation</a></li> <li><a href="/wiki/Computational_complexity_theory" title="Computational complexity theory">Computational complexity theory</a></li> <li><a href="/wiki/Numerical_analysis" title="Numerical analysis">Numerical analysis</a></li> <li><a href="/wiki/Mathematical_optimization" title="Mathematical optimization">Optimization</a></li> <li><a href="/wiki/Computer_algebra" title="Computer algebra">Computer algebra</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Lists_of_mathematics_topics" title="Lists of mathematics topics">Related topics</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Mathematicians" class="mw-redirect" title="Mathematicians">Mathematicians</a> <ul><li><a href="/wiki/List_of_mathematicians" class="mw-redirect" title="List of mathematicians">lists</a></li></ul></li> <li><a href="/wiki/Informal_mathematics" title="Informal mathematics">Informal mathematics</a></li> <li><a href="/wiki/List_of_films_about_mathematicians" title="List of films about mathematicians">Films about mathematicians</a></li> <li><a href="/wiki/Recreational_mathematics" title="Recreational mathematics">Recreational mathematics</a></li> <li><a href="/wiki/Mathematics_and_art" title="Mathematics and art">Mathematics and art</a></li> <li><a href="/wiki/Mathematics_education" title="Mathematics education">Mathematics education</a></li></ul> </div></td></tr><tr><td class="navbox-abovebelow" colspan="2"><div> <ul><li><b><span 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src="//upload.wikimedia.org/wikipedia/en/thumb/9/96/Symbol_category_class.svg/16px-Symbol_category_class.svg.png" decoding="async" width="16" height="16" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/9/96/Symbol_category_class.svg/23px-Symbol_category_class.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/9/96/Symbol_category_class.svg/31px-Symbol_category_class.svg.png 2x" data-file-width="180" data-file-height="185" /></span></span> <b><a href="/wiki/Category:Fields_of_mathematics" title="Category:Fields of mathematics">Category</a></b></li> <li><span class="noviewer" typeof="mw:File"><span title="Commons page"><img alt="" src="//upload.wikimedia.org/wikipedia/en/thumb/4/4a/Commons-logo.svg/12px-Commons-logo.svg.png" decoding="async" width="12" height="16" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/4/4a/Commons-logo.svg/18px-Commons-logo.svg.png 1.5x, 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class="navbox-styles"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236075235"></div><div role="navigation" class="navbox" aria-labelledby="Microeconomics" style="padding:3px"><table class="nowraplinks hlist mw-collapsible autocollapse navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1239400231"><div class="navbar plainlinks hlist navbar-mini"><ul><li class="nv-view"><a href="/wiki/Template:Microeconomics" title="Template:Microeconomics"><abbr title="View this template">v</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:Microeconomics" title="Template talk:Microeconomics"><abbr title="Discuss this template">t</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:EditPage/Template:Microeconomics" title="Special:EditPage/Template:Microeconomics"><abbr title="Edit this template">e</abbr></a></li></ul></div><div id="Microeconomics" style="font-size:114%;margin:0 4em"><a href="/wiki/Microeconomics" title="Microeconomics">Microeconomics</a></div></th></tr><tr><th scope="row" class="navbox-group" style="width:1%">Major topics</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Aggregation_problem" title="Aggregation problem">Aggregation</a></li> <li><a href="/wiki/Budget_set" title="Budget set">Budget set</a></li> <li><a href="/wiki/Consumer_choice" title="Consumer choice">Consumer choice</a></li> <li><a href="/wiki/Convexity_in_economics" title="Convexity in economics">Convexity</a> and <a href="/wiki/Non-convexity_(economics)" title="Non-convexity (economics)">non-convexity</a></li> <li><a href="/wiki/Economic_cost" title="Economic cost">Cost</a> <ul><li><a href="/wiki/Average_cost" title="Average cost">Average</a></li> <li><a href="/wiki/Marginal_cost" title="Marginal cost">Marginal</a></li> <li><a href="/wiki/Opportunity_cost" title="Opportunity cost">Opportunity</a> <ul><li><a href="/wiki/Implicit_cost" title="Implicit cost">Implicit</a></li></ul></li> <li><a href="/wiki/Social_cost" title="Social cost">Social</a></li> <li><a href="/wiki/Sunk_cost" title="Sunk cost">Sunk</a></li> <li><a href="/wiki/Transaction_cost" title="Transaction cost">Transaction</a></li></ul></li> <li><a href="/wiki/Cost%E2%80%93benefit_analysis" title="Cost–benefit analysis">Cost–benefit analysis</a></li> <li><a href="/wiki/Deadweight_loss" title="Deadweight loss">Deadweight loss</a></li> <li><a href="/wiki/Distribution_(economics)" title="Distribution (economics)">Distribution</a></li> <li><a href="/wiki/Economies_of_scale" title="Economies of scale">Economies of scale</a></li> <li><a href="/wiki/Economies_of_scope" title="Economies of scope">Economies of scope</a></li> <li><a href="/wiki/Elasticity_(economics)" title="Elasticity (economics)">Elasticity</a> <ul><li><a href="/wiki/Cross_elasticity_of_demand" title="Cross elasticity of demand">Cross elasticity of demand</a></li> <li><a href="/wiki/Income_elasticity_of_demand" title="Income elasticity of demand">Income elasticity of demand</a></li> <li><a href="/wiki/Price_elasticity_of_demand" title="Price elasticity of demand">Price elasticity of demand</a></li> <li><a href="/wiki/Price_elasticity_of_supply" title="Price elasticity of supply">Price elasticity of supply</a></li></ul></li> <li><a href="/wiki/Economic_equilibrium" title="Economic equilibrium">Equilibrium</a> <ul><li><a href="/wiki/General_equilibrium_theory" title="General equilibrium theory">General</a></li></ul></li> <li><a href="/wiki/Trade" title="Trade">Exchange</a></li> <li><a href="/wiki/Externality" title="Externality">Externality</a></li> <li><a href="/wiki/Theory_of_the_firm" title="Theory of the firm">Firms</a></li> <li><a href="/wiki/Goods_and_services" title="Goods and services">Goods and services</a> <ul><li><a href="/wiki/Goods" title="Goods">Goods</a></li> <li><a href="/wiki/Service_(economics)" title="Service (economics)">Service</a></li></ul></li> <li><a href="/wiki/Family_economics" title="Family economics">Household</a></li> <li><a href="/wiki/Income%E2%80%93consumption_curve" title="Income–consumption curve">Income–consumption curve</a></li> <li><a href="/wiki/Information_economics" title="Information economics">Information</a></li> <li><a href="/wiki/Indifference_curve" title="Indifference curve">Indifference curve</a></li> <li><a href="/wiki/Intertemporal_choice" title="Intertemporal choice">Intertemporal choice</a></li> <li><a href="/wiki/Market_(economics)" title="Market (economics)">Market</a></li> <li><a href="/wiki/Market_failure" title="Market failure">Market failure</a></li> <li><a href="/wiki/Market_structure" title="Market structure">Market structure</a> <ul><li><a href="/wiki/Competition_(economics)" title="Competition (economics)">Competition</a> <ul><li><a href="/wiki/Monopolistic_competition" title="Monopolistic competition">Monopolistic</a></li> <li><a href="/wiki/Perfect_competition" title="Perfect competition">Perfect</a></li></ul></li> <li><a href="/wiki/Duopoly" title="Duopoly">Duopoly</a></li> <li><a href="/wiki/Monopoly" title="Monopoly">Monopoly</a> <ul><li><a href="/wiki/Bilateral_monopoly" title="Bilateral monopoly">Bilateral</a></li> <li><a href="/wiki/Complementary_monopoly" title="Complementary monopoly">Complementary</a></li></ul></li> <li><a href="/wiki/Monopsony" title="Monopsony">Monopsony</a></li> <li><a href="/wiki/Oligopoly" title="Oligopoly">Oligopoly</a></li> <li><a href="/wiki/Oligopsony" title="Oligopsony">Oligopsony</a></li></ul></li> <li><a href="/wiki/Pareto_efficiency" title="Pareto efficiency">Pareto efficiency</a></li> <li><a href="/wiki/Preference_(economics)" title="Preference (economics)">Preferences</a></li> <li><a href="/wiki/Price" title="Price">Price</a> <ul><li><a href="/wiki/Price_controls" title="Price controls">Price controls</a></li> <li><a href="/wiki/Price_ceiling" title="Price ceiling">Price ceiling</a></li> <li><a href="/wiki/Price_floor" title="Price floor">Price floor</a></li> <li><a href="/wiki/Price_discrimination" title="Price discrimination">Price discrimination</a></li> <li><a href="/wiki/Price_signal" title="Price signal">Price signal</a></li> <li><a href="/wiki/Price_system" title="Price system">Price system</a>/<a href="/wiki/Free_price_system" title="Free price system">Free</a></li> <li><a href="/wiki/Pricing" title="Pricing">Pricing</a></li></ul></li> <li><a href="/wiki/Production_set" title="Production set">Production</a></li> <li><a href="/wiki/Profit_(economics)" title="Profit (economics)">Profit</a></li> <li><a href="/wiki/Public_good_(economics)" title="Public good (economics)">Public goods</a></li> <li><a href="/wiki/Rationing" title="Rationing">Rationing</a></li> <li><a href="/wiki/Economic_rent" title="Economic rent">Rent</a></li> <li><a href="/wiki/Returns_to_scale" title="Returns to scale">Returns to scale</a></li> <li><a href="/wiki/Risk_aversion" title="Risk aversion">Risk aversion</a></li> <li><a href="/wiki/Scarcity" title="Scarcity">Scarcity</a></li> <li><a href="/wiki/Shortage" title="Shortage">Shortage</a>/<a href="/wiki/Excess_supply" title="Excess supply">Excess supply</a></li> <li><a href="/wiki/Substitution_effect" title="Substitution effect">Substitution effect</a></li> <li><a href="/wiki/Economic_surplus" title="Economic surplus">Surplus</a></li> <li><a href="/wiki/Social_choice_theory" title="Social choice theory">Social choice</a></li> <li><a href="/wiki/Supply_and_demand" title="Supply and demand">Supply and demand</a> <ul><li><a href="/wiki/Demand" title="Demand">Demand</a>/<a href="/wiki/Law_of_demand" title="Law of demand">Law of demand</a></li> <li><a href="/wiki/Supply_(economics)" title="Supply (economics)">Supply</a>/<a href="/wiki/Law_of_supply" title="Law of supply">Law of supply</a></li></ul></li> <li><a href="/wiki/Uncertainty" title="Uncertainty">Uncertainty</a></li> <li><a href="/wiki/Utility" title="Utility">Utility</a> <ul><li><a href="/wiki/Expected_utility_hypothesis" title="Expected utility hypothesis">Expected</a></li> <li><a href="/wiki/Marginal_utility" title="Marginal utility">Marginal</a></li></ul></li> <li><a href="/wiki/Wage" title="Wage">Wage</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Subfields</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Behavioral_economics" title="Behavioral economics">Behavioral</a></li> <li><a href="/wiki/Business_economics" title="Business economics">Business</a></li> <li><a href="/wiki/Computational_economics" title="Computational economics">Computational</a></li> <li><a href="/wiki/Development_economics" title="Development economics">Development</a></li> <li><a href="/wiki/Statistical_decision_theory" class="mw-redirect" title="Statistical decision theory">Statistical decision theory</a></li> <li><a href="/wiki/Econometrics" title="Econometrics">Econometrics</a></li> <li><a href="/wiki/Engineering_economics" title="Engineering economics">Engineering economics</a></li> <li><a href="/wiki/Engineering_economics_(civil_engineering)" title="Engineering economics (civil engineering)">Civil engineering economics</a></li> <li><a href="/wiki/Evolutionary_economics" title="Evolutionary economics">Evolutionary</a></li> <li><a href="/wiki/Experimental_economics" title="Experimental economics">Experimental</a></li> <li><a class="mw-selflink selflink">Game theory</a></li> <li><a href="/wiki/Green_economy" title="Green economy">Green</a></li> <li><a href="/wiki/Industrial_organization" title="Industrial organization">Industrial organization</a></li> <li><a href="/wiki/Institutional_economics" title="Institutional economics">Institutional</a></li> <li><a href="/wiki/Labour_economics" title="Labour economics">Labor</a></li> <li><a href="/wiki/Law_and_economics" title="Law and economics">Law</a></li> <li><a href="/wiki/Managerial_economics" title="Managerial economics">Managerial</a></li> <li><a href="/wiki/Mathematical_economics" title="Mathematical economics">Mathematical</a></li> <li><a href="/wiki/Microfoundations" title="Microfoundations">Microfoundations of macroeconomics</a></li> <li><a href="/wiki/Operations_research" title="Operations research">Operations research</a></li> <li><a href="/wiki/Mathematical_optimization" title="Mathematical optimization">Optimization</a></li> <li><a href="/wiki/Welfare_economics" title="Welfare economics">Welfare</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">See also</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Economics" title="Economics">Economics</a> <ul><li><a href="/wiki/Applied_economics" title="Applied economics">Applied</a></li></ul></li> <li><a href="/wiki/Macroeconomics" title="Macroeconomics">Macroeconomics</a></li> <li><a href="/wiki/Political_economy" title="Political economy">Political economy</a></li></ul> </div></td></tr><tr><td class="navbox-abovebelow" colspan="2"><div> <ul><li><span class="nowrap"><span class="noviewer" typeof="mw:File"><a href="/wiki/File:Emblem-money.svg" class="mw-file-description"><img alt="icon" src="//upload.wikimedia.org/wikipedia/commons/thumb/f/f3/Emblem-money.svg/16px-Emblem-money.svg.png" decoding="async" width="16" height="16" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/f/f3/Emblem-money.svg/24px-Emblem-money.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/f/f3/Emblem-money.svg/32px-Emblem-money.svg.png 2x" data-file-width="48" data-file-height="48" /></a></span> </span><a href="/wiki/Portal:Business" title="Portal:Business">Business portal</a></li> <li><span class="noviewer" typeof="mw:File"><span title="Category"><img alt="" src="//upload.wikimedia.org/wikipedia/en/thumb/9/96/Symbol_category_class.svg/16px-Symbol_category_class.svg.png" decoding="async" width="16" height="16" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/9/96/Symbol_category_class.svg/23px-Symbol_category_class.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/9/96/Symbol_category_class.svg/31px-Symbol_category_class.svg.png 2x" data-file-width="180" data-file-height="185" /></span></span> <a href="/wiki/Category:Microeconomics" title="Category:Microeconomics">Category</a></li></ul> </div></td></tr></tbody></table></div> <div class="navbox-styles"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236075235"><style data-mw-deduplicate="TemplateStyles:r886047488">.mw-parser-output .nobold{font-weight:normal}</style></div><div role="navigation" class="navbox" aria-labelledby="Property" style="padding:3px"><table class="nowraplinks hlist mw-collapsible mw-collapsed navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1239400231"><div class="navbar plainlinks hlist navbar-mini"><ul><li class="nv-view"><a href="/wiki/Template:Property_navbox" title="Template:Property navbox"><abbr title="View this template">v</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:Property_navbox" title="Template talk:Property navbox"><abbr title="Discuss this template">t</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:EditPage/Template:Property_navbox" title="Special:EditPage/Template:Property navbox"><abbr title="Edit this template">e</abbr></a></li></ul></div><div id="Property" style="font-size:114%;margin:0 4em"><a href="/wiki/Property" title="Property">Property</a></div></th></tr><tr><th scope="row" class="navbox-group" style="width:1%">By owner</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Collective_ownership" title="Collective ownership">Collective</a></li> <li><a href="/wiki/Common_ownership" title="Common ownership">Common</a></li> <li><a href="/wiki/Communal_land" title="Communal land">Communal</a></li> <li><a href="/wiki/Community_property" title="Community property">Community</a></li> <li><a href="/wiki/Crown_land" title="Crown land">Crown</a></li> <li><a href="/wiki/Customary_land" title="Customary land">Customary</a></li> <li><a href="/wiki/Cooperative" title="Cooperative">Cooperative</a></li> <li><a href="/wiki/Private_property" title="Private property">Private</a></li> <li><a href="/wiki/Public_property" title="Public property">Public</a></li> <li><a href="/wiki/Self-ownership" title="Self-ownership">Self</a></li> <li><a href="/wiki/Social_ownership" title="Social ownership">Social</a></li> <li><a href="/wiki/State_ownership" title="State ownership">State</a></li> <li><a href="/wiki/Unowned_property" title="Unowned property">Unowned</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">By nature</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Croft_(land)" title="Croft (land)">Croft</a></li> <li><a href="/wiki/Estate_in_land" title="Estate in land">Estate (landed)</a></li> <li><a href="/wiki/Intangible_property" title="Intangible property">Intangible</a></li> <li><a href="/wiki/Intellectual_property" title="Intellectual property">Intellectual</a> <ul><li><a href="/wiki/Indigenous_intellectual_property" title="Indigenous intellectual property">indigenous</a></li></ul></li> <li><a href="/wiki/Personal_property" title="Personal property">Personal</a></li> <li><a href="/wiki/Tangible_property" title="Tangible property">Tangible</a> <ul><li><a href="/wiki/Real_property" title="Real property">real</a></li></ul></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Commons" title="Commons">Commons</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Common_land" title="Common land">Common land</a></li> <li><a href="/wiki/Common-pool_resource" title="Common-pool resource">Common-pool resource</a></li> <li><a href="/wiki/Digital_commons_(economics)" title="Digital commons (economics)">Digital</a></li> <li><a href="/wiki/Global_commons" title="Global commons">Global</a></li> <li><a href="/wiki/Information_commons" title="Information commons">Information</a></li> <li><a href="/wiki/Knowledge_commons" title="Knowledge commons">Knowledge</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Theory</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Bundle_of_rights" title="Bundle of rights">Bundle of rights</a></li> <li><a href="/wiki/Commodity" title="Commodity">Commodity</a> <ul><li><a href="/wiki/Fictitious_commodities" title="Fictitious commodities">fictitious commodities</a></li></ul></li> <li><a href="/wiki/Common_good_(economics)" title="Common good (economics)">Common good (economics)</a></li> <li><a href="/wiki/Excludability" title="Excludability">Excludability</a></li> <li><a href="/wiki/First_possession_theory_of_property" title="First possession theory of property">First possession</a> <ul><li><a href="/wiki/Original_appropriation" title="Original appropriation">appropriation</a></li> <li><a href="/wiki/Homestead_principle" title="Homestead principle">homestead principle</a></li></ul></li> <li><a href="/wiki/Free-rider_problem" title="Free-rider problem">Free-rider problem</a></li> <li><a class="mw-selflink selflink">Game theory</a></li> <li><a href="/wiki/Georgism" title="Georgism">Georgism</a></li> <li><a href="/wiki/Gift_economy" title="Gift economy">Gift economy</a></li> <li><a href="/wiki/Labor_theory_of_property" title="Labor theory of property">Labor theory of property</a></li> <li><a href="/wiki/Law_of_rent" title="Law of rent">Law of rent</a> <ul><li><a href="/wiki/Rent-seeking" title="Rent-seeking">rent-seeking</a></li></ul></li> <li><a href="/wiki/Legal_plunder" class="mw-redirect" title="Legal plunder">Legal plunder</a></li> <li><a href="/wiki/Natural_rights_and_legal_rights" title="Natural rights and legal rights">Natural rights</a></li> <li><a href="/wiki/Ownership" title="Ownership">Ownership</a></li> <li><a href="/wiki/Property_rights_(economics)" title="Property rights (economics)">Property rights</a> <ul><li><a href="/wiki/Primogeniture" title="Primogeniture">primogeniture</a></li> <li><a href="/wiki/Usufruct" title="Usufruct">usufruct</a></li> <li><a href="/wiki/Women%27s_property_rights" title="Women's property rights">women's</a></li></ul></li> <li><a href="/wiki/Right_to_property" title="Right to property">Right to property</a></li> <li><a href="/wiki/Rivalry_(economics)" title="Rivalry (economics)">Rivalry</a></li> <li><a href="/wiki/Tragedy_of_the_commons" title="Tragedy of the commons">Tragedy of the commons</a> <ul><li><a href="/wiki/Tragedy_of_the_anticommons" title="Tragedy of the anticommons">anticommons</a></li></ul></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Applications</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><td colspan="2" class="navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Acequia" title="Acequia"><i>Acequia</i> (watercourse)</a></li> <li><a href="/wiki/Ejido" title="Ejido"><i>Ejido</i> (agrarian land)</a></li> <li><a href="/wiki/Estate_(law)" title="Estate (law)">Estate</a> <ul><li><a href="/wiki/Estate_(law)" title="Estate (law)">legal</a></li> <li><a href="/wiki/Literary_estate" title="Literary estate">literary</a></li> <li><a href="/wiki/Real_estate" title="Real estate">real</a></li></ul></li> <li><a href="/wiki/List_of_types_of_formally_designated_forests" title="List of types of formally designated forests">Forest types</a></li> <li><i><a href="/wiki/Huerta" title="Huerta">Huerta</a></i></li> <li><a href="/wiki/Inheritance" title="Inheritance">Inheritance</a> <ul><li><a href="/wiki/Executor" title="Executor">executor</a></li></ul></li> <li><a href="/wiki/Land_tenure" title="Land tenure">Land tenure</a></li> <li><a href="/wiki/Property_law" title="Property law">Property law</a> <ul><li><a href="/wiki/Alienation_(property_law)" title="Alienation (property law)">alienation</a></li> <li><a href="/wiki/Easement" title="Easement">easement</a></li> <li><a href="/wiki/Restraint_on_alienation" title="Restraint on alienation">restraint on alienation</a></li> <li><a href="/wiki/Real_estate" title="Real estate">real estate</a></li> <li><a href="/wiki/Title_(property)" title="Title (property)">title</a></li></ul></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Rights</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Air_rights" title="Air rights">Air</a></li> <li><a href="/wiki/Exclusive_economic_zone" title="Exclusive economic zone">Fishing</a></li> <li><a href="/wiki/The_Scheduled_Tribes_and_Other_Traditional_Forest_Dwellers_(Recognition_of_Forest_Rights)_Act,_2006" title="The Scheduled Tribes and Other Traditional Forest Dwellers (Recognition of Forest Rights) Act, 2006">Forest-dwelling (India)</a></li> <li><a href="/wiki/Freedom_to_roam" title="Freedom to roam">Freedom to roam</a></li> <li><a href="/wiki/Grazing_rights" title="Grazing rights">Grazing</a> <ul><li><a href="/wiki/Pannage" title="Pannage">pannage</a></li></ul></li> <li><a href="/wiki/Hunting" title="Hunting">Hunting</a></li> <li><a href="/wiki/Land_law#Land_rights" title="Land law">Land</a> <ul><li><a href="/wiki/Aboriginal_title" title="Aboriginal title">aboriginal</a></li> <li><a href="/wiki/Indigenous_land_rights" title="Indigenous land rights">indigenous</a></li> <li><a href="/wiki/Squatting" title="Squatting">squatting</a></li></ul></li> <li><a href="/wiki/Littoral_rights" title="Littoral rights">Littoral</a></li> <li><a href="/wiki/Mineral_rights" title="Mineral rights">Mineral</a> <ul><li><i><a href="/wiki/Bergregal" title="Bergregal">Bergregal</a></i></li></ul></li> <li><a href="/wiki/Right_of_way_(transit)" class="mw-redirect" title="Right of way (transit)">Right of way (transit)</a></li> <li><a href="/wiki/Right_of_way_(property_access)" class="mw-redirect" title="Right of way (property access)">Right of way (property access)</a></li> <li><a href="/wiki/Water_right" title="Water right">Water</a> <ul><li><a href="/wiki/Prior-appropriation_water_rights" title="Prior-appropriation water rights">prior-appropriation</a></li> <li><a href="/wiki/Riparian_water_rights" title="Riparian water rights">riparian</a></li></ul></li></ul> </div></td></tr></tbody></table><div></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Accumulation_by_dispossession" title="Accumulation by dispossession">Disposession</a>/<br /><a href="/wiki/Redistribution_of_income_and_wealth" title="Redistribution of income and wealth">redistribution</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Bioprospecting" title="Bioprospecting">Bioprospecting</a> <ul><li><a href="/wiki/Biopiracy" title="Biopiracy">biopiracy</a></li></ul></li> <li><a href="/wiki/Collectivization_in_the_Soviet_Union" title="Collectivization in the Soviet Union">Collectivization</a></li> <li><a href="/wiki/Eminent_domain" title="Eminent domain">Eminent domain</a></li> <li><a href="/wiki/Enclosure" title="Enclosure">Enclosure</a></li> <li><a href="/wiki/Eviction" title="Eviction">Eviction</a></li> <li><a href="/wiki/Expropriation" class="mw-redirect" title="Expropriation">Expropriation</a></li> <li><i><a href="/wiki/Farhud" title="Farhud">Farhud</a></i></li> <li><a href="/wiki/Forced_displacement" title="Forced displacement">Forced migration</a> <ul><li><a href="/wiki/Population_transfer" title="Population transfer">population transfer</a></li> <li><a href="/wiki/Repatriation" title="Repatriation">repatriation</a></li></ul></li> <li><a href="/wiki/Illegal,_unreported_and_unregulated_fishing" title="Illegal, unreported and unregulated fishing">Illegal fishing</a></li> <li><a href="/wiki/Illegal_logging" title="Illegal logging">Illegal logging</a></li> <li><a href="/wiki/Land_Back" title="Land Back">Land Back</a></li> <li><a href="/wiki/Land_reform" title="Land reform">Land reform</a></li> <li><a href="/wiki/Legal_plunder" class="mw-redirect" title="Legal plunder">Legal plunder</a></li> <li><a href="/wiki/Piracy" title="Piracy">Piracy</a></li> <li><a href="/wiki/Poaching" title="Poaching">Poaching</a></li> <li><a href="/wiki/Primitive_accumulation_of_capital" title="Primitive accumulation of capital">Primitive accumulation</a></li> <li><a href="/wiki/Privatization" title="Privatization">Privatization</a></li> <li><a href="/wiki/Regulatory_taking" class="mw-redirect" title="Regulatory taking">Regulatory taking</a></li> <li><a href="/wiki/Slavery" title="Slavery">Slavery</a> <ul><li><a href="/wiki/Bride_buying" title="Bride buying">bride buying</a></li> <li><a href="/wiki/Human_trafficking" title="Human trafficking">human trafficking</a></li> <li>spousal <ul><li><a href="/wiki/Husband-selling" class="mw-redirect" title="Husband-selling">husband-selling</a></li> <li><a href="/wiki/Wife_selling" title="Wife selling">wife selling</a></li></ul></li> <li><a href="/wiki/Wage_slavery" title="Wage slavery">wage</a></li></ul></li> <li><a href="/wiki/Tax" title="Tax">Tax</a> <ul><li><a href="/wiki/Inheritance_tax" title="Inheritance tax">inheritance</a></li> <li><a href="/wiki/Poll_tax" title="Poll tax">poll</a></li> <li><a href="/wiki/Progressive_tax" title="Progressive tax">progressive</a></li> <li><a href="/wiki/Property_tax" title="Property tax">property</a></li></ul></li> <li><a href="/wiki/Theft" title="Theft">Theft</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Scholars<br /><span class="nobold">(<i>key work</i>)</span></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Fr%C3%A9d%C3%A9ric_Bastiat" title="Frédéric Bastiat">Frédéric Bastiat</a> <ul><li><i><a href="/wiki/The_Law_(Bastiat_book)" title="The Law (Bastiat book)">The Law</a></i></li></ul></li> <li><a href="/wiki/Ronald_Coase" title="Ronald Coase">Ronald Coase</a></li> <li><a href="/wiki/Friedrich_Engels" title="Friedrich Engels">Friedrich Engels</a> <ul><li><i><a href="/wiki/The_Origin_of_the_Family,_Private_Property_and_the_State" title="The Origin of the Family, Private Property and the State">The Origin of the Family, Private Property and the State</a></i></li></ul></li> <li><a href="/wiki/Henry_George" title="Henry George">Henry George</a> <ul><li><i><a href="/wiki/Progress_and_Poverty" title="Progress and Poverty">Progress and Poverty</a></i></li></ul></li> <li><a href="/wiki/Garrett_Hardin" title="Garrett Hardin">Garrett Hardin</a></li> <li><a href="/wiki/David_Harvey" title="David Harvey">David Harvey</a></li> <li><a href="/wiki/John_Locke" title="John Locke">John Locke</a> <ul><li><i><a href="/wiki/Two_Treatises_of_Government" title="Two Treatises of Government">Two Treatises of Government</a></i></li></ul></li> <li><a href="/wiki/Karl_Marx" title="Karl Marx">Karl Marx</a> <ul><li><i><a href="/wiki/Das_Kapital" title="Das Kapital">Das Kapital</a></i></li></ul></li> <li><a href="/wiki/Marcel_Mauss" title="Marcel Mauss">Marcel Mauss</a> <ul><li><i><a href="/wiki/The_Gift_(essay)" title="The Gift (essay)">The Gift</a></i></li></ul></li> <li><a href="/wiki/John_Stuart_Mill" title="John Stuart Mill">John Stuart Mill</a></li> <li><a href="/wiki/Elinor_Ostrom" title="Elinor Ostrom">Elinor Ostrom</a></li> <li><a href="/wiki/Karl_Polanyi" title="Karl Polanyi">Karl Polanyi</a> <ul><li><i><a href="/wiki/The_Great_Transformation_(book)" title="The Great Transformation (book)">The Great Transformation</a></i></li></ul></li> <li><a href="/wiki/Pierre-Joseph_Proudhon" title="Pierre-Joseph Proudhon">Pierre-Joseph Proudhon</a> <ul><li><i><a href="/wiki/Property_is_theft!" class="mw-redirect" title="Property is theft!">What Is Property?</a></i></li></ul></li> <li><a href="/wiki/David_Ricardo" title="David Ricardo">David Ricardo</a></li> <li><a href="/wiki/Murray_Rothbard" title="Murray Rothbard">Murray N. Rothbard</a> <ul><li><i><a href="/wiki/The_Ethics_of_Liberty" title="The Ethics of Liberty">The Ethics of Liberty</a></i></li></ul></li> <li><a href="/wiki/Jean-Jacques_Rousseau" title="Jean-Jacques Rousseau">Jean-Jacques Rousseau</a> <ul><li><i><a href="/wiki/The_Social_Contract" title="The Social Contract">The Social Contract</a></i></li></ul></li> <li><a href="/wiki/Adam_Smith" title="Adam Smith">Adam Smith</a> <ul><li><i><a href="/wiki/The_Wealth_of_Nations" title="The Wealth of Nations">The Wealth of Nations</a></i></li></ul></li></ul> </div></td></tr><tr><td class="navbox-abovebelow" colspan="2"><div> <ul><li><span class="noviewer" typeof="mw:File"><span title="Category"><img alt="" src="//upload.wikimedia.org/wikipedia/en/thumb/9/96/Symbol_category_class.svg/16px-Symbol_category_class.svg.png" decoding="async" width="16" height="16" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/9/96/Symbol_category_class.svg/23px-Symbol_category_class.svg.png 1.5x, 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[\"CITEREFBeck2008\"] = 1,\n [\"CITEREFBellhouse,_David_R.2007\"] = 1,\n [\"CITEREFBellhouse2015\"] = 1,\n [\"CITEREFBen-DavidBorodinKarpTardos1994\"] = 1,\n [\"CITEREFBergDickhautMcCabe1995\"] = 1,\n [\"CITEREFBhatLeyton-Brown2012\"] = 1,\n [\"CITEREFBicchieri1989\"] = 1,\n [\"CITEREFBicchieri1993\"] = 1,\n [\"CITEREFBicchieri2006\"] = 1,\n [\"CITEREFBraithwaite1955\"] = 1,\n [\"CITEREFBrams1994\"] = 1,\n [\"CITEREFBrams2001\"] = 1,\n [\"CITEREFBrandenburger\"] = 1,\n [\"CITEREFBruin2005\"] = 1,\n [\"CITEREFCamerer1997\"] = 1,\n [\"CITEREFCamerer2003\"] = 4,\n [\"CITEREFCamerer2008\"] = 1,\n [\"CITEREFCamererLoewensteinRabin2011\"] = 1,\n [\"CITEREFChaffin2018\"] = 1,\n [\"CITEREFChandrasekaran\"] = 1,\n [\"CITEREFChang2015\"] = 1,\n [\"CITEREFChangPiraveenanPattisonProkopenko2020\"] = 1,\n [\"CITEREFChastainLivnatPapadimitriouVazirani2014\"] = 1,\n [\"CITEREFChevalier-RoignantTrigeorgis2012\"] = 1,\n [\"CITEREFChristen1998\"] = 1,\n [\"CITEREFClempner2006\"] = 1,\n [\"CITEREFCournot1838\"] = 1,\n [\"CITEREFDolevPanagopoulouRabieSchiller2011\"] = 1,\n [\"CITEREFDowns1957\"] = 1,\n [\"CITEREFDutta1999\"] = 1,\n [\"CITEREFEdgeworth1881\"] = 1,\n [\"CITEREFFarquharson1969\"] = 1,\n [\"CITEREFFearon1995\"] = 1,\n [\"CITEREFFels1961\"] = 1,\n [\"CITEREFFerguson\"] = 1,\n [\"CITEREFFernandezBierman1998\"] = 1,\n [\"CITEREFFisher1930\"] = 1,\n [\"CITEREFFriedman1998\"] = 1,\n [\"CITEREFFudenberg2006\"] = 1,\n [\"CITEREFFudenbergTirole1991\"] = 1,\n [\"CITEREFGaffalPadilla_Gálvez2014\"] = 1,\n [\"CITEREFGauthier1986\"] = 1,\n [\"CITEREFGeneserethLovePell2005\"] = 1,\n [\"CITEREFGibbons1992\"] = 2,\n [\"CITEREFGibbons2001\"] = 1,\n [\"CITEREFGintis2000\"] = 1,\n [\"CITEREFGreenMas-ColellWhinston1995\"] = 1,\n [\"CITEREFGrimKokalisAlai-TaftiKilb2004\"] = 1,\n [\"CITEREFGuzman1996\"] = 1,\n [\"CITEREFHalpern2008\"] = 1,\n [\"CITEREFHanley2021\"] = 1,\n [\"CITEREFHarperMaynard_Smith2003\"] = 1,\n [\"CITEREFHarsanyi1961\"] = 1,\n [\"CITEREFHazraAnjaria2022\"] = 1,\n [\"CITEREFHearnDemaine2009\"] = 1,\n [\"CITEREFHeinlein1959\"] = 1,\n [\"CITEREFHoRajagopalanSkvortsovArulampalam2022\"] = 1,\n [\"CITEREFHoward1971\"] = 1,\n [\"CITEREFIsaacs1999\"] = 1,\n [\"CITEREFJohnsonMislin2011\"] = 1,\n [\"CITEREFJones2008\"] = 1,\n [\"CITEREFJoseph_Y._Halpern2008\"] = 1,\n [\"CITEREFJörg_Bewersdorff2005\"] = 1,\n [\"CITEREFKadaneLarkey1983\"] = 1,\n [\"CITEREFKavka1986\"] = 1,\n [\"CITEREFKearnsLittmanSingh2011\"] = 1,\n [\"CITEREFKim2014\"] = 1,\n [\"CITEREFKollerMegiddovon_Stengel1994\"] = 1,\n [\"CITEREFKollerPfeffer1997\"] = 1,\n [\"CITEREFKreps1990\"] = 1,\n [\"CITEREFKuhn1997\"] = 1,\n [\"CITEREFKuhn2004\"] = 1,\n [\"CITEREFLarson2021\"] = 1,\n [\"CITEREFLeonard2010\"] = 1,\n [\"CITEREFLevyRazin2004\"] = 1,\n [\"CITEREFLewis1969\"] = 1,\n [\"CITEREFLeyton-BrownTennenholtz2005\"] = 1,\n [\"CITEREFLittmanLittman2007\"] = 1,\n [\"CITEREFLozovanuPickl2015\"] = 1,\n [\"CITEREFLuceRaiffa1957\"] = 1,\n [\"CITEREFMaynard_Smith1974\"] = 1,\n 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[\"CITEREFPlottSmith2008\"] = 1,\n [\"CITEREFPoundstone1993\"] = 1,\n [\"CITEREFQinStuart1997\"] = 1,\n [\"CITEREFQuine1960\"] = 1,\n [\"CITEREFQuine1967\"] = 1,\n [\"CITEREFR._Duncan_LuceHoward_Raiffa1989\"] = 1,\n [\"CITEREFRapoport1987\"] = 1,\n [\"CITEREFRasmusen2007\"] = 1,\n [\"CITEREFReid1982\"] = 1,\n [\"CITEREFRoberts2020\"] = 1,\n [\"CITEREFRosenthal1973\"] = 1,\n [\"CITEREFRoss2006\"] = 1,\n [\"CITEREFSandholm2008\"] = 1,\n [\"CITEREFSannikov2007\"] = 1,\n [\"CITEREFSatterthwaite1975\"] = 1,\n [\"CITEREFShapiro1989\"] = 1,\n [\"CITEREFShapley1953\"] = 1,\n [\"CITEREFShapleyShubik1971\"] = 1,\n [\"CITEREFShoham2008\"] = 1,\n [\"CITEREFShohamLeyton-Brown2008\"] = 1,\n [\"CITEREFShohamLeyton-Brown2009\"] = 1,\n [\"CITEREFShor\"] = 1,\n [\"CITEREFShor2006\"] = 1,\n [\"CITEREFShubik1981\"] = 1,\n [\"CITEREFShubik2002\"] = 1,\n [\"CITEREFSiegfried2006\"] = 1,\n [\"CITEREFSingh1998\"] = 1,\n [\"CITEREFSkyrms1990\"] = 2,\n [\"CITEREFSkyrms1996\"] = 1,\n [\"CITEREFSkyrms2004\"] = 1,\n [\"CITEREFSmith1992\"] = 1,\n [\"CITEREFSmith2001\"] = 1,\n [\"CITEREFSoberWilson1998\"] = 1,\n [\"CITEREFSpulber1995\"] = 1,\n [\"CITEREFStalnaker1996\"] = 1,\n [\"CITEREFTagiew2008\"] = 1,\n [\"CITEREFTagiew2009\"] = 1,\n [\"CITEREFTagiew2011\"] = 1,\n [\"CITEREFTesfatsion2006\"] = 1,\n [\"CITEREFThrallLucas1963\"] = 1,\n [\"CITEREFTirole1988\"] = 1,\n [\"CITEREFTomlinLygerosShankar_Sastry2000\"] = 1,\n [\"CITEREFUllmann-Margalit1977\"] = 1,\n [\"CITEREFVelegolSuheyConnollyMorrissey2018\"] = 1,\n [\"CITEREFWatson2013\"] = 1,\n [\"CITEREFWebb2007\"] = 1,\n [\"CITEREFWilkinson2005\"] = 1,\n [\"CITEREFWilliams2013\"] = 1,\n [\"CITEREFWood2011\"] = 1,\n [\"CITEREFZermelo1913\"] = 2,\n [\"CITEREFvon_Neumann1928\"] = 2,\n [\"CITEREFvon_Neumann1959\"] = 1,\n [\"CITEREFvon_NeumannMorgenstern1944\"] = 1,\n [\"Economics\"] = 1,\n}\ntemplate_list = table#1 {\n [\"!\"] = 3,\n [\"'\"] = 1,\n [\"About\"] = 1,\n [\"Anchor\"] = 1,\n [\"Annotated link\"] = 19,\n [\"ArXiv\"] = 2,\n [\"Areas of mathematics\"] = 1,\n [\"Authority control\"] = 1,\n [\"Cbignore\"] = 2,\n [\"Citation\"] = 52,\n [\"Citation needed\"] = 3,\n [\"Cite AV media\"] = 1,\n [\"Cite arXiv\"] = 3,\n [\"Cite book\"] = 61,\n [\"Cite conference\"] = 3,\n [\"Cite encyclopedia\"] = 3,\n [\"Cite journal\"] = 48,\n [\"Cite news\"] = 4,\n [\"Cite thesis\"] = 1,\n [\"Cite web\"] = 21,\n [\"Color\"] = 12,\n [\"Commons category\"] = 1,\n [\"Conflict resolution sidebar\"] = 1,\n [\"DEFAULTSORT:Game Theory\"] = 1,\n [\"Diagonal split header\"] = 5,\n [\"Doi\"] = 1,\n [\"Economics sidebar\"] = 1,\n [\"Efn\"] = 4,\n [\"Frac\"] = 2,\n [\"Game theory\"] = 1,\n [\"Harv\"] = 2,\n [\"Harvard citations\"] = 3,\n [\"Harvtxt\"] = 5,\n [\"ISBN\"] = 1,\n [\"Isbn\"] = 3,\n [\"Lang\"] = 3,\n [\"Longitem\"] = 3,\n [\"Main\"] = 18,\n [\"Math\"] = 1,\n [\"Microeconomics\"] = 1,\n [\"Nbsp\"] = 1,\n [\"Notelist\"] = 1,\n [\"Page needed\"] = 9,\n [\"Payoff matrix\"] = 6,\n [\"Property navbox\"] = 1,\n [\"Reflist\"] = 1,\n [\"See also\"] = 2,\n [\"Sfn\"] = 1,\n [\"Sfnp\"] = 9,\n [\"Short description\"] = 1,\n [\"Springer\"] = 1,\n [\"Strategy\"] = 1,\n [\"Toclimit\"] = 1,\n [\"Use American English\"] = 1,\n [\"Use dmy dates\"] = 1,\n [\"Var\"] = 7,\n [\"Varserif\"] = 3,\n [\"Webarchive\"] = 12,\n [\"Who\"] = 2,\n [\"Wikibooks\"] = 1,\n [\"Wikiquote\"] = 2,\n [\"Wikiversity\"] = 1,\n [\"Wiktionary\"] = 1,\n}\narticle_whitelist = table#1 {\n}\ntable#1 {\n [\"size\"] = \"tiny\",\n}\ntable#1 {\n [\"size\"] = \"tiny\",\n}\n","limitreport-profile":[["MediaWiki\\Extension\\Scribunto\\Engines\\LuaSandbox\\LuaSandboxCallback::callParserFunction","280","14.3"],["?","260","13.3"],["MediaWiki\\Extension\\Scribunto\\Engines\\LuaSandbox\\LuaSandboxCallback::sub","160","8.2"],["MediaWiki\\Extension\\Scribunto\\Engines\\LuaSandbox\\LuaSandboxCallback::gsub","140","7.1"],["recursiveClone 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