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id="toc-Classical_game_theory" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Classical_game_theory"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.1</span> <span>Classical game theory</span> </div> </a> <ul id="toc-Classical_game_theory-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-The_problem_of_ritualized_behaviour" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#The_problem_of_ritualized_behaviour"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.2</span> <span>The problem of ritualized behaviour</span> </div> </a> <ul id="toc-The_problem_of_ritualized_behaviour-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Adapting_game_theory_to_evolutionary_games" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Adapting_game_theory_to_evolutionary_games"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.3</span> <span>Adapting game theory to evolutionary games</span> </div> </a> <ul id="toc-Adapting_game_theory_to_evolutionary_games-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Evolutionary_games" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Evolutionary_games"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>Evolutionary games</span> </div> </a> <button aria-controls="toc-Evolutionary_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 Evolutionary games subsection</span> </button> <ul id="toc-Evolutionary_games-sublist" class="vector-toc-list"> <li id="toc-Models" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Models"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.1</span> <span>Models</span> </div> </a> <ul id="toc-Models-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Hawk_dove" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Hawk_dove"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.2</span> <span>Hawk dove</span> </div> </a> <ul id="toc-Hawk_dove-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-War_of_attrition" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#War_of_attrition"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.3</span> <span>War of attrition</span> </div> </a> <ul id="toc-War_of_attrition-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Asymmetries_that_allow_new_strategies" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Asymmetries_that_allow_new_strategies"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.4</span> <span>Asymmetries that allow new strategies</span> </div> </a> <ul id="toc-Asymmetries_that_allow_new_strategies-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Social_behaviour" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Social_behaviour"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.5</span> <span>Social behaviour</span> </div> </a> <ul id="toc-Social_behaviour-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Contests_of_selfish_genes" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Contests_of_selfish_genes"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Contests of selfish genes</span> </div> </a> <button aria-controls="toc-Contests_of_selfish_genes-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 Contests of selfish genes subsection</span> </button> <ul id="toc-Contests_of_selfish_genes-sublist" class="vector-toc-list"> <li id="toc-Eusociality_and_kin_selection" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Eusociality_and_kin_selection"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.1</span> <span>Eusociality and kin selection</span> </div> </a> <ul id="toc-Eusociality_and_kin_selection-sublist" class="vector-toc-list"> </ul> </li> <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">3.2</span> <span>Prisoner's dilemma</span> </div> </a> <ul id="toc-Prisoner's_dilemma-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Routes_to_altruism" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Routes_to_altruism"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.3</span> <span>Routes to altruism</span> </div> </a> <ul id="toc-Routes_to_altruism-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-The_evolutionarily_stable_strategy" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#The_evolutionarily_stable_strategy"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.4</span> <span>The evolutionarily stable strategy</span> </div> </a> <ul id="toc-The_evolutionarily_stable_strategy-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Unstable_games,_cyclic_patterns" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Unstable_games,_cyclic_patterns"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>Unstable games, cyclic patterns</span> </div> </a> <button aria-controls="toc-Unstable_games,_cyclic_patterns-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 Unstable games, cyclic patterns subsection</span> </button> <ul id="toc-Unstable_games,_cyclic_patterns-sublist" class="vector-toc-list"> <li id="toc-Rock_paper_scissors" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Rock_paper_scissors"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.1</span> <span>Rock paper scissors</span> </div> </a> <ul id="toc-Rock_paper_scissors-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Side-blotched_lizard_plays_the_RPS,_and_other_cyclical_games" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Side-blotched_lizard_plays_the_RPS,_and_other_cyclical_games"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.2</span> <span>Side-blotched lizard plays the RPS, and other cyclical games</span> </div> </a> <ul id="toc-Side-blotched_lizard_plays_the_RPS,_and_other_cyclical_games-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Signalling,_sexual_selection_and_the_handicap_principle" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Signalling,_sexual_selection_and_the_handicap_principle"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>Signalling, sexual selection and the handicap principle</span> </div> </a> <ul id="toc-Signalling,_sexual_selection_and_the_handicap_principle-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Coevolution" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Coevolution"> <div class="vector-toc-text"> <span class="vector-toc-numb">6</span> <span>Coevolution</span> </div> </a> <ul id="toc-Coevolution-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Extending_the_model" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Extending_the_model"> <div class="vector-toc-text"> <span class="vector-toc-numb">7</span> <span>Extending the model</span> </div> </a> <button aria-controls="toc-Extending_the_model-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 Extending the model subsection</span> </button> <ul id="toc-Extending_the_model-sublist" class="vector-toc-list"> <li id="toc-Spatial_games" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Spatial_games"> <div class="vector-toc-text"> <span class="vector-toc-numb">7.1</span> <span>Spatial games</span> </div> </a> <ul id="toc-Spatial_games-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Effects_of_having_information" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Effects_of_having_information"> <div class="vector-toc-text"> <span class="vector-toc-numb">7.2</span> <span>Effects of having information</span> </div> </a> <ul id="toc-Effects_of_having_information-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Finite_populations" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Finite_populations"> <div class="vector-toc-text"> <span class="vector-toc-numb">7.3</span> <span>Finite populations</span> </div> </a> <ul id="toc-Finite_populations-sublist" class="vector-toc-list"> </ul> </li> </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">8</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">9</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">10</span> <span>References</span> </div> </a> <ul id="toc-References-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> <ul id="toc-Further_reading-sublist" class="vector-toc-list"> </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 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class="vector-unpinned-container"> </div> </div> </div> </nav> <h1 id="firstHeading" class="firstHeading mw-first-heading"><span class="mw-page-title-main">Evolutionary 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 14 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-14" 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">14 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_%D8%A7%D9%84%D8%AA%D8%B7%D9%88%D8%B1%D9%8A%D8%A9" title="نظرية الألعاب التطورية – Arabic" lang="ar" hreflang="ar" data-title="نظرية الألعاب التطورية" data-language-autonym="العربية" data-language-local-name="Arabic" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/Teoria_evolutiva_de_jocs" title="Teoria evolutiva de jocs – Catalan" lang="ca" hreflang="ca" data-title="Teoria evolutiva de 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/Evolu%C4%8Dn%C3%AD_teorie_her" title="Evoluční teorie her – Czech" lang="cs" hreflang="cs" data-title="Evoluční 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-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Evolution%C3%A4re_Spieltheorie" title="Evolutionäre Spieltheorie – German" lang="de" hreflang="de" data-title="Evolutionäre 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/Evolutsiooniline_m%C3%A4nguteooria" title="Evolutsiooniline mänguteooria – Estonian" lang="et" hreflang="et" data-title="Evolutsiooniline mänguteooria" data-language-autonym="Eesti" data-language-local-name="Estonian" class="interlanguage-link-target"><span>Eesti</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/Teor%C3%ADa_evolutiva_de_juegos" title="Teoría evolutiva de juegos – Spanish" lang="es" hreflang="es" data-title="Teoría evolutiva 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-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_%D9%81%D8%B1%DA%AF%D8%B4%D8%AA%DB%8C" title="نظریه بازی فرگشتی – Persian" lang="fa" hreflang="fa" data-title="نظریه بازی فرگشتی" 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_%C3%A9volutive_des_jeux" title="Théorie évolutive des jeux – French" lang="fr" hreflang="fr" data-title="Théorie évolutive 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-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%EC%A7%84%ED%99%94_%EA%B2%8C%EC%9E%84_%EC%9D%B4%EB%A1%A0" title="진화 게임 이론 – Korean" lang="ko" hreflang="ko" data-title="진화 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-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Teoria_evolutiva_dei_giochi" title="Teoria evolutiva dei giochi – Italian" lang="it" hreflang="it" data-title="Teoria evolutiva 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-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Evolutionaire_speltheorie" title="Evolutionaire speltheorie – Dutch" lang="nl" hreflang="nl" data-title="Evolutionaire 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 mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E9%80%B2%E5%8C%96%E3%82%B2%E3%83%BC%E3%83%A0" title="進化ゲーム – Japanese" lang="ja" 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data-event-name="pinnable-header.vector-appearance.unpin">hide</button> </div> </div> </div> </nav> </div> </div> <div id="bodyContent" class="vector-body" aria-labelledby="firstHeading" data-mw-ve-target-container> <div class="vector-body-before-content"> <div class="mw-indicators"> </div> <div 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">Application of game theory to evolving populations in biology</div> <p><b>Evolutionary game theory</b> (<b>EGT</b>) is the application of <a href="/wiki/Game_theory" title="Game theory">game theory</a> to evolving populations in <a href="/wiki/Biology" title="Biology">biology</a>. It defines a framework of contests, strategies, and analytics into which <a href="/wiki/Darwinism" title="Darwinism">Darwinian</a> competition can be modelled. It originated in 1973 with <a href="/wiki/John_Maynard_Smith" title="John Maynard Smith">John Maynard Smith</a> and <a href="/wiki/George_R._Price" title="George R. Price">George R. Price</a>'s formalisation of contests, analysed as strategies, and the mathematical criteria that can be used to predict the results of competing strategies.<sup id="cite_ref-Price_1-0" class="reference"><a href="#cite_note-Price-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> </p><p>Evolutionary game theory differs from classical game theory in focusing more on the dynamics of strategy change.<sup id="cite_ref-Newton2018renaissance_2-0" class="reference"><a href="#cite_note-Newton2018renaissance-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> This is influenced by the frequency of the competing strategies in the population.<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> </p><p>Evolutionary game theory has helped to explain the basis of <a href="/wiki/Altruism_(biology)" title="Altruism (biology)">altruistic</a> behaviours in Darwinian <a href="/wiki/Evolution" title="Evolution">evolution</a>. It has in turn become of interest to <a href="/wiki/Economists" class="mw-redirect" title="Economists">economists</a>,<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> <a href="/wiki/Sociologists" class="mw-redirect" title="Sociologists">sociologists</a>, <a href="/wiki/Anthropologists" class="mw-redirect" title="Anthropologists">anthropologists</a>, and <a href="/wiki/Philosophers" class="mw-redirect" title="Philosophers">philosophers</a>. </p> <meta property="mw:PageProp/toc" /> <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=Evolutionary_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="Classical_game_theory">Classical game theory</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Evolutionary_game_theory&action=edit&section=2" title="Edit section: Classical game theory"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></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">Main article: <a href="/wiki/Game_theory" title="Game theory">Game theory</a></div> <p>Classical <a href="/wiki/Non-cooperative_game_theory" title="Non-cooperative game theory">non-cooperative game theory</a> was conceived by <a href="/wiki/John_von_Neumann" title="John von Neumann">John von Neumann</a> to determine optimal strategies in competitions between adversaries. A contest involves players, all of whom have a choice of moves. Games can be a single round or repetitive. The approach a player takes in making their moves constitutes their strategy. Rules govern the outcome for the moves taken by the players, and outcomes produce payoffs for the players; rules and resulting payoffs can be expressed as <a href="/wiki/Decision_tree" title="Decision tree">decision trees</a> or in a <a href="/wiki/Matrix_(mathematics)" title="Matrix (mathematics)">payoff matrix</a>. Classical theory requires the players to make rational choices. Each player must consider the strategic analysis that their opponents are making to make their own choice of moves.<sup id="cite_ref-5" class="reference"><a href="#cite_note-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> <div class="mw-heading mw-heading3"><h3 id="The_problem_of_ritualized_behaviour">The problem of ritualized behaviour</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Evolutionary_game_theory&action=edit&section=3" title="Edit section: The problem of ritualized behaviour"><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:John_Maynard_Smith.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/e/e2/John_Maynard_Smith.jpg/220px-John_Maynard_Smith.jpg" decoding="async" width="220" height="220" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/e/e2/John_Maynard_Smith.jpg/330px-John_Maynard_Smith.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/e/e2/John_Maynard_Smith.jpg/440px-John_Maynard_Smith.jpg 2x" data-file-width="767" data-file-height="766" /></a><figcaption>The mathematical biologist <a href="/wiki/John_Maynard_Smith" title="John Maynard Smith">John Maynard Smith</a> modelled evolutionary games.</figcaption></figure> <p>Evolutionary game theory started with the problem of how to explain ritualized animal behaviour in a conflict situation; "why are animals so 'gentlemanly or ladylike' in contests for resources?" The leading <a href="/wiki/Ethologists" class="mw-redirect" title="Ethologists">ethologists</a> <a href="/wiki/Niko_Tinbergen" class="mw-redirect" title="Niko Tinbergen">Niko Tinbergen</a> and <a href="/wiki/Konrad_Lorenz" title="Konrad Lorenz">Konrad Lorenz</a> proposed that such behaviour exists <a href="/wiki/Group_selection" title="Group selection">for the benefit of the species</a>. <a href="/wiki/John_Maynard_Smith" title="John Maynard Smith">John Maynard Smith</a> considered that incompatible with Darwinian thought,<sup id="cite_ref-7" class="reference"><a href="#cite_note-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup> where selection occurs at an individual level, so self-interest is rewarded while seeking the common good is not. Maynard Smith, a mathematical biologist, turned to game theory as suggested by George Price, though <a href="/wiki/Richard_Lewontin" title="Richard Lewontin">Richard Lewontin</a>'s attempts to use the theory had failed.<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> <div class="mw-heading mw-heading3"><h3 id="Adapting_game_theory_to_evolutionary_games">Adapting game theory to evolutionary games</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Evolutionary_game_theory&action=edit&section=4" title="Edit section: Adapting game theory to evolutionary games"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Maynard Smith realised that an evolutionary version of game theory does not require players to act rationally—only that they have a strategy. The results of a game show how good that strategy was, just as <a href="/wiki/Evolution" title="Evolution">evolution</a> tests alternative strategies for the ability to survive and reproduce. In biology, strategies are genetically inherited traits that control an individual's action, analogous with computer programs. The success of a strategy is determined by how good the strategy is in the presence of competing strategies (including itself), and of the frequency with which those strategies are used.<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> Maynard Smith described his work in his 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-JMSbook_10-0" class="reference"><a href="#cite_note-JMSbook-10"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup> </p><p>Participants aim to produce as many replicas of themselves as they can, and the payoff is in units of fitness (relative worth in being able to reproduce). It is always a multi-player game with many competitors. Rules include replicator dynamics, in other words how the fitter players will spawn more replicas of themselves into the population and how the less fit will be <a href="/wiki/Culling" title="Culling">culled</a>, in a <a href="/wiki/Replicator_equation" title="Replicator equation">replicator equation</a>. The replicator dynamics models heredity but not mutation, and assumes asexual reproduction for the sake of simplicity. Games are run repetitively with no terminating conditions. Results include the dynamics of changes in the population, the success of strategies, and any equilibrium states reached. Unlike in classical game theory, players do not choose their strategy and cannot change it: they are born with a strategy and their offspring inherit that same strategy.<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> </p> <div class="mw-heading mw-heading2"><h2 id="Evolutionary_games">Evolutionary games</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Evolutionary_game_theory&action=edit&section=5" title="Edit section: Evolutionary games"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="Models">Models</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Evolutionary_game_theory&action=edit&section=6" title="Edit section: Models"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure typeof="mw:File/Thumb"><a href="/wiki/File:Game_Diagram_AniFin.gif" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/0/02/Game_Diagram_AniFin.gif/400px-Game_Diagram_AniFin.gif" decoding="async" width="400" height="300" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/0/02/Game_Diagram_AniFin.gif/600px-Game_Diagram_AniFin.gif 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/0/02/Game_Diagram_AniFin.gif/800px-Game_Diagram_AniFin.gif 2x" data-file-width="960" data-file-height="720" /></a><figcaption>Evolutionary game theory analyses Darwinian mechanisms with a <a href="/wiki/System_model" class="mw-redirect" title="System model">system model</a> with three main components – <i>population</i>, <i>game</i>, and <i>replicator dynamics</i>. The system process has four phases:<br /> <br /> 1) The model (as evolution itself) deals with a <i>population</i> (Pn). The population will exhibit <a href="/wiki/Evolution#Sources_of_variation" title="Evolution">variation</a> among competing individuals. In the model this competition is represented by the game.<br /> <br /> 2) The game tests the strategies of the individuals under the rules of the game. These rules produce different payoffs – in units of <a href="/wiki/Fitness_(biology)" title="Fitness (biology)">fitness</a> (the production rate of offspring). The contesting individuals meet in pairwise contests with others, normally in a highly mixed distribution of the population. The mix of strategies in the population affects the payoff results by altering the odds that any individual may meet up in contests with various strategies. The individuals leave the game pairwise contest with a resulting fitness determined by the contest outcome, represented in a <i>payoff matrix</i>.<br /> <br /> 3) Based on this resulting fitness each member of the population then undergoes replication or culling determined by the exact mathematics of the <i>replicator dynamics process</i>. This overall process then produces a <i>new generation</i> P(n+1). Each surviving individual now has a new fitness level determined by the game result.<br /> <br /> 4) The new generation then takes the place of the previous one and the cycle repeats. The population mix may converge to an <i>evolutionarily stable state</i> that cannot be invaded by any mutant strategy.</figcaption></figure> <p>Evolutionary game theory encompasses Darwinian evolution, including competition (the game), natural selection (replicator dynamics), and heredity. Evolutionary game theory has contributed to the understanding of <a href="/wiki/Group_selection" title="Group selection">group selection</a>, <a href="/wiki/Sexual_selection" title="Sexual selection">sexual selection</a>, <a href="/wiki/Altruism" title="Altruism">altruism</a>, <a href="/wiki/Parental_care" title="Parental care">parental care</a>, <a href="/wiki/Co-evolution" class="mw-redirect" title="Co-evolution">co-evolution</a>, and <a href="/wiki/Ecology" title="Ecology">ecological</a> dynamics. Many counter-intuitive situations in these areas have been put on a firm mathematical footing by the use of these models.<sup id="cite_ref-Hammerstein_12-0" class="reference"><a href="#cite_note-Hammerstein-12"><span class="cite-bracket">[</span>12<span class="cite-bracket">]</span></a></sup> </p><p>The common way to study the evolutionary dynamics in games is through <a href="/wiki/Replicator_equation" title="Replicator equation">replicator equations</a>. These show the growth rate of the proportion of organisms using a certain strategy and that rate is equal to the difference between the average payoff of that strategy and the average payoff of the population as a whole.<sup id="cite_ref-Samuelson_13-0" class="reference"><a href="#cite_note-Samuelson-13"><span class="cite-bracket">[</span>13<span class="cite-bracket">]</span></a></sup> Continuous replicator equations assume infinite populations, <a href="/wiki/Continuous_time" class="mw-redirect" title="Continuous time">continuous time</a>, <a href="/wiki/Complete_mixing" title="Complete mixing">complete mixing</a> and that strategies breed true. Some <a href="/wiki/Attractor" title="Attractor">attractors</a> (all global asymptotically stable fixed points) of the equations are <a href="/wiki/Evolutionarily_stable_state" title="Evolutionarily stable state">evolutionarily stable states</a>.<sup id="cite_ref-Zeeman_14-0" class="reference"><a href="#cite_note-Zeeman-14"><span class="cite-bracket">[</span>14<span class="cite-bracket">]</span></a></sup> A strategy which can survive all "mutant" strategies is considered evolutionarily stable. In the context of animal behavior, this usually means such strategies are programmed and heavily influenced by <a href="/wiki/Genetics" title="Genetics">genetics</a>, thus making any player or organism's strategy determined by these biological factors.<sup id="cite_ref-15" class="reference"><a href="#cite_note-15"><span class="cite-bracket">[</span>15<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-16" class="reference"><a href="#cite_note-16"><span class="cite-bracket">[</span>16<span class="cite-bracket">]</span></a></sup> </p><p>Evolutionary games are mathematical objects with different rules, payoffs, and mathematical behaviours. Each "game" represents different problems that organisms have to deal with, and the strategies they might adopt to survive and reproduce. Evolutionary games are often given colourful names and cover stories which describe the general situation of a particular game. Representative games include <a href="/wiki/Chicken_(game)" title="Chicken (game)">hawk-dove</a>,<sup id="cite_ref-Price_1-1" class="reference"><a href="#cite_note-Price-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> <a href="/wiki/War_of_attrition_(game)" title="War of attrition (game)">war of attrition</a>,<sup id="cite_ref-SelfishGene_17-0" class="reference"><a href="#cite_note-SelfishGene-17"><span class="cite-bracket">[</span>17<span class="cite-bracket">]</span></a></sup> <a href="/wiki/Stag_hunt" title="Stag hunt">stag hunt</a>, <a href="/wiki/Cheating_(biology)" title="Cheating (biology)">producer-scrounger</a>, <a href="/wiki/Tragedy_of_the_commons" title="Tragedy of the commons">tragedy of the commons</a>, and <a href="/wiki/Prisoner%27s_dilemma" title="Prisoner's dilemma">prisoner's dilemma</a>. Strategies for these games include hawk, dove, bourgeois, prober, defector, assessor, and retaliator. The various strategies compete under the particular game's rules, and the mathematics are used to determine the results and behaviours. </p> <div class="mw-heading mw-heading3"><h3 id="Hawk_dove">Hawk dove</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Evolutionary_game_theory&action=edit&section=7" title="Edit section: Hawk dove"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure typeof="mw:File/Thumb"><a href="/wiki/File:HawkDove2.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/c/c3/HawkDove2.jpg/300px-HawkDove2.jpg" decoding="async" width="300" height="225" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/c/c3/HawkDove2.jpg/450px-HawkDove2.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/c/c3/HawkDove2.jpg/600px-HawkDove2.jpg 2x" data-file-width="964" data-file-height="722" /></a><figcaption> Solution of the <a href="/wiki/Chicken_(game)" title="Chicken (game)">hawk dove</a> game for V=2, C=10 and fitness starting base B=4. The fitness of a hawk for different population mixes is plotted as a black line, that of dove in red. An ESS (a stationary point) will exist when hawk and dove fitness are equal: Hawks are 20% of population and doves are 80% of the population.</figcaption></figure> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Chicken_(game)" title="Chicken (game)">Chicken (game)</a></div> <p>The first game that <a href="/wiki/Maynard_Smith" class="mw-redirect" title="Maynard Smith">Maynard Smith</a> analysed is the classic <i><a href="/wiki/Chicken_(game)" title="Chicken (game)">hawk dove</a></i><sup id="cite_ref-18" class="reference"><a href="#cite_note-18"><span class="cite-bracket">[</span>a<span class="cite-bracket">]</span></a></sup> game. It was conceived to analyse Lorenz and Tinbergen's problem, a contest over a shareable resource. The contestants can be either a hawk or a dove. These are two subtypes or morphs of one species with different strategies. The hawk first displays aggression, then escalates into a fight until it either wins or is injured (loses). The dove first displays aggression, but if faced with major escalation runs for safety. If not faced with such escalation, the dove attempts to share the resource.<sup id="cite_ref-Price_1-2" class="reference"><a href="#cite_note-Price-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> </p> <table class="wikitable" style="text-align:center"> <caption style="white-space:nowrap">Payoff matrix for hawk dove game </caption> <tbody><tr> <td></td> <td><b> meets hawk </b></td> <td><b> meets dove </b> </td></tr> <tr> <td><b>if hawk</b></td> <td>V/2 − C/2</td> <td>V </td></tr> <tr> <td><b>if dove</b></td> <td>0</td> <td>V/2 </td></tr></tbody></table> <p>Given that the resource is given the value V, the damage from losing a fight is given cost C:<sup id="cite_ref-Price_1-3" class="reference"><a href="#cite_note-Price-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> </p> <ul><li>If a hawk meets a dove, the hawk gets the full resource V</li> <li>If a hawk meets a hawk, half the time they win, half the time they lose, so the average outcome is then V/2 minus C/2</li> <li>If a dove meets a hawk, the dove will back off and get nothing – 0</li> <li>If a dove meets a dove, both share the resource and get V/2</li></ul> <p>The actual payoff, however, depends on the probability of meeting a hawk or dove, which in turn is a representation of the percentage of hawks and doves in the population when a particular contest takes place. That, in turn, is determined by the results of all of the previous contests. If the cost of losing C is greater than the value of winning V (the normal situation in the natural world) the mathematics ends in an <a href="/wiki/Evolutionarily_stable_strategy" title="Evolutionarily stable strategy">evolutionarily stable strategy</a> (ESS), a mix of the two strategies where the population of hawks is V/C. The population regresses to this equilibrium point if any new hawks or doves make a temporary perturbation in the population. The solution of the hawk dove game explains why most animal contests involve only <a href="/wiki/Ritualized_aggression" title="Ritualized aggression">ritual fighting</a> behaviours in contests rather than outright battles. The result does not at all depend on "<a href="/wiki/Group_selection" title="Group selection">good of the species</a>" behaviours as suggested by Lorenz, but solely on the implication of actions of so-called <a href="/wiki/Selfish_genes" class="mw-redirect" title="Selfish genes">selfish genes</a>.<sup id="cite_ref-Price_1-4" class="reference"><a href="#cite_note-Price-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="War_of_attrition">War of attrition</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Evolutionary_game_theory&action=edit&section=8" title="Edit section: War of attrition"><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/War_of_attrition_(game)" title="War of attrition (game)">War of attrition (game)</a></div> <p>In the hawk dove game the resource is shareable, which gives payoffs to both doves meeting in a pairwise contest. Where the resource is not shareable, but an alternative resource might be available by backing off and trying elsewhere, pure hawk or dove strategies are less effective. If an unshareable resource is combined with a high cost of losing a contest (injury or possible death) both hawk and dove payoffs are further diminished. A safer strategy of lower cost display, bluffing and waiting to win, is then viable – a bluffer strategy. The game then becomes one of accumulating costs, either the costs of displaying or the costs of prolonged unresolved engagement. It is effectively an auction; the winner is the contestant who will swallow the greater cost while the loser gets the same cost as the winner but no resource.<sup id="cite_ref-SelfishGene_17-1" class="reference"><a href="#cite_note-SelfishGene-17"><span class="cite-bracket">[</span>17<span class="cite-bracket">]</span></a></sup> The resulting evolutionary game theory mathematics lead to an optimal strategy of timed bluffing.<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> <figure typeof="mw:File/Thumb"><a href="/wiki/File:Attrition_graph.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/5/5b/Attrition_graph.jpg/300px-Attrition_graph.jpg" decoding="async" width="300" height="225" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/5/5b/Attrition_graph.jpg/450px-Attrition_graph.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/5/5b/Attrition_graph.jpg/600px-Attrition_graph.jpg 2x" data-file-width="960" data-file-height="720" /></a><figcaption> <a href="/wiki/War_of_attrition_(game)" title="War of attrition (game)">War of attrition</a> for different values of resource. Note the time it takes for an accumulation of 50% of the contestants to quit vs. the value (V) of resource contested for.</figcaption></figure> <p>This is because in the war of attrition any strategy that is unwavering and predictable is unstable, because it will ultimately be displaced by a mutant strategy which relies on the fact that it can best the existing predictable strategy by investing an extra small delta of waiting resource to ensure that it wins. Therefore, only a random unpredictable strategy can maintain itself in a population of bluffers. The contestants in effect choose an acceptable cost to be incurred related to the value of the resource being sought, effectively making a random bid as part of a mixed strategy (a strategy where a contestant has several, or even many, possible actions in their strategy). This implements a distribution of bids for a resource of specific value V, where the bid for any specific contest is chosen at random from that distribution. The distribution (an ESS) can be computed using the <a href="/wiki/Bishop-Cannings_theorem" class="mw-redirect" title="Bishop-Cannings theorem">Bishop-Cannings theorem</a>, which holds true for any mixed-strategy ESS.<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> The distribution function in these contests was determined by Parker and Thompson to be: </p> <dl><dd><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 p(x)={\frac {e^{-x/V}}{V}}.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>p</mi> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msup> <mi>e</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mi>V</mi> </mrow> </msup> <mi>V</mi> </mfrac> </mrow> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle p(x)={\frac {e^{-x/V}}{V}}.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/dd8bec4966d9bbb45aa77361c679352eb195cd50" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; margin-left: -0.089ex; width:14.6ex; height:5.843ex;" alt="{\displaystyle p(x)={\frac {e^{-x/V}}{V}}.}"></span></dd></dl> <p>The result is that the cumulative population of quitters for any particular cost m in this "mixed strategy" solution is: </p> <dl><dd><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 p(m)=1-e^{-m/V},}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>p</mi> <mo stretchy="false">(</mo> <mi>m</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mn>1</mn> <mo>−</mo> <msup> <mi>e</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mi>V</mi> </mrow> </msup> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle p(m)=1-e^{-m/V},}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/045b50191e4afb51b4415c09e016424dbdddc1d8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; margin-left: -0.089ex; width:18.98ex; height:3.343ex;" alt="{\displaystyle p(m)=1-e^{-m/V},}"></span></dd></dl> <p>as shown in the adjacent graph. The intuitive sense that greater values of resource sought leads to greater waiting times is borne out. This is observed in nature, as in male dung flies contesting for mating sites, where the timing of disengagement in contests is as predicted by evolutionary theory mathematics.<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> </p> <div class="mw-heading mw-heading3"><h3 id="Asymmetries_that_allow_new_strategies">Asymmetries that allow new strategies</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Evolutionary_game_theory&action=edit&section=9" title="Edit section: Asymmetries that allow new strategies"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1237032888/mw-parser-output/.tmulti">.mw-parser-output .tmulti .multiimageinner{display:flex;flex-direction:column}.mw-parser-output .tmulti .trow{display:flex;flex-direction:row;clear:left;flex-wrap:wrap;width:100%;box-sizing:border-box}.mw-parser-output .tmulti .tsingle{margin:1px;float:left}.mw-parser-output .tmulti .theader{clear:both;font-weight:bold;text-align:center;align-self:center;background-color:transparent;width:100%}.mw-parser-output .tmulti .thumbcaption{background-color:transparent}.mw-parser-output .tmulti .text-align-left{text-align:left}.mw-parser-output .tmulti .text-align-right{text-align:right}.mw-parser-output .tmulti .text-align-center{text-align:center}@media all and (max-width:720px){.mw-parser-output .tmulti .thumbinner{width:100%!important;box-sizing:border-box;max-width:none!important;align-items:center}.mw-parser-output .tmulti .trow{justify-content:center}.mw-parser-output .tmulti .tsingle{float:none!important;max-width:100%!important;box-sizing:border-box;text-align:center}.mw-parser-output .tmulti .tsingle .thumbcaption{text-align:left}.mw-parser-output .tmulti .trow>.thumbcaption{text-align:center}}@media screen{html.skin-theme-clientpref-night .mw-parser-output .tmulti .multiimageinner img{background-color:white}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .tmulti .multiimageinner img{background-color:white}}</style><div class="thumb tmulti tright"><div class="thumbinner multiimageinner" style="width:408px;max-width:408px"><div class="trow"><div class="tsingle" style="width:202px;max-width:202px"><div class="thumbimage"><span typeof="mw:File"><a href="/wiki/File:Scatophaga_stercoraria.jpg" class="mw-file-description"><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/3/39/Scatophaga_stercoraria.jpg/200px-Scatophaga_stercoraria.jpg" decoding="async" width="200" height="141" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/3/39/Scatophaga_stercoraria.jpg/300px-Scatophaga_stercoraria.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/3/39/Scatophaga_stercoraria.jpg/400px-Scatophaga_stercoraria.jpg 2x" data-file-width="2640" data-file-height="1858" /></a></span></div><div class="thumbcaption">Dung fly (<i>Scatophaga stercoraria</i>) – a war of attrition player</div></div><div class="tsingle" style="width:202px;max-width:202px"><div class="thumbimage"><span typeof="mw:File"><a href="/wiki/File:30-EastTimor-Dive2_Maubara_35_(Mantis_Shrimp)-APiazza.JPG" class="mw-file-description"><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/4/47/30-EastTimor-Dive2_Maubara_35_%28Mantis_Shrimp%29-APiazza.JPG/200px-30-EastTimor-Dive2_Maubara_35_%28Mantis_Shrimp%29-APiazza.JPG" decoding="async" width="200" height="128" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/47/30-EastTimor-Dive2_Maubara_35_%28Mantis_Shrimp%29-APiazza.JPG/300px-30-EastTimor-Dive2_Maubara_35_%28Mantis_Shrimp%29-APiazza.JPG 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/47/30-EastTimor-Dive2_Maubara_35_%28Mantis_Shrimp%29-APiazza.JPG/400px-30-EastTimor-Dive2_Maubara_35_%28Mantis_Shrimp%29-APiazza.JPG 2x" data-file-width="889" data-file-height="568" /></a></span></div><div class="thumbcaption">The mantis shrimp guarding its home with the bourgeois strategy</div></div></div><div class="trow" style="display:flex"><div class="thumbcaption">Animal strategy examples: by examining the behaviours, then determining both the costs and the values of resources attained in a contest the strategy of an organism can be verified</div></div></div></div> <p>In the war of attrition there must be nothing that signals the size of a bid to an opponent, otherwise the opponent can use the cue in an effective counter-strategy. There is however a mutant strategy which can better a bluffer in the <a href="/wiki/War_of_attrition_(game)" title="War of attrition (game)">war of attrition</a> game if a suitable asymmetry exists, the bourgeois strategy. Bourgeois uses an asymmetry of some sort to break the deadlock. In nature one such asymmetry is possession of a resource. The strategy is to play a hawk if in possession of the resource, but to display then retreat if not in possession. This requires greater cognitive capability than hawk, but bourgeois is common in many animal contests, such as in contests among <a href="/wiki/Mantis_shrimp" title="Mantis shrimp">mantis shrimps</a> and among <a href="/wiki/Speckled_wood_butterfly" class="mw-redirect" title="Speckled wood butterfly">speckled wood butterflies</a>. </p> <div class="mw-heading mw-heading3"><h3 id="Social_behaviour">Social behaviour</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Evolutionary_game_theory&action=edit&section=10" title="Edit section: Social behaviour"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure typeof="mw:File/Thumb"><a href="/wiki/File:Game_Theory_Strategic_Social_Alternatives.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/e/eb/Game_Theory_Strategic_Social_Alternatives.jpg/300px-Game_Theory_Strategic_Social_Alternatives.jpg" decoding="async" width="300" height="214" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/e/eb/Game_Theory_Strategic_Social_Alternatives.jpg/450px-Game_Theory_Strategic_Social_Alternatives.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/e/eb/Game_Theory_Strategic_Social_Alternatives.jpg/600px-Game_Theory_Strategic_Social_Alternatives.jpg 2x" data-file-width="1332" data-file-height="949" /></a><figcaption>Alternatives for game theoretic social interaction</figcaption></figure> <p>Games like hawk dove and war of attrition represent pure competition between individuals and have no attendant social elements. Where social influences apply, competitors have four possible alternatives for strategic interaction. This is shown on the adjacent figure, where a plus sign represents a benefit and a minus sign represents a cost. </p> <ul><li>In a <i>cooperative</i> or <i>mutualistic</i> relationship both "donor" and "recipient" are almost indistinguishable as both gain a benefit in the game by co-operating, i.e. the pair are in a game-wise situation where both can gain by executing a certain strategy, or alternatively both must act in concert because of some encompassing constraints that effectively puts them "in the same boat".</li> <li>In an <i>altruistic</i> relationship the donor, at a cost to themself provides a benefit to the recipient. In the general case the recipient will have a kin relationship to the donor and the donation is one-way. Behaviours where benefits are donated alternatively (in both directions) at a cost, are often called "altruistic", but on analysis such "altruism" can be seen to arise from optimised "selfish" strategies.</li> <li><i>Spite</i> is essentially a “reversed” form of cooperation where neither party receives a tangible benefit. The general case is that the ally is kin related and the benefit is an easier competitive environment for the ally. <small>Note: George Price, one of the early mathematical modellers of both altruism and spite, found this equivalence particularly disturbing at an emotional level.</small><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></li> <li><i>Selfishness</i> is the base criteria of all strategic choice from a game theory perspective – strategies not aimed at self-survival and self-replication are not long for any game. Critically however, this situation is impacted by the fact that competition is taking place on multiple levels – i.e. at a genetic, an individual and a group level.</li></ul> <div class="mw-heading mw-heading2"><h2 id="Contests_of_selfish_genes">Contests of selfish genes</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Evolutionary_game_theory&action=edit&section=11" title="Edit section: Contests of selfish genes"><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:Spermophilus_beldingi.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/f/f1/Spermophilus_beldingi.jpg/170px-Spermophilus_beldingi.jpg" decoding="async" width="170" height="207" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/f/f1/Spermophilus_beldingi.jpg/255px-Spermophilus_beldingi.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/f/f1/Spermophilus_beldingi.jpg/340px-Spermophilus_beldingi.jpg 2x" data-file-width="446" data-file-height="543" /></a><figcaption>Female <a href="/wiki/Belding%27s_ground_squirrel" title="Belding's ground squirrel">Belding's ground squirrels</a> risk their lives giving loud alarm calls, protecting closely related female colony members; males are less closely related and do not call.<sup id="cite_ref-23" class="reference"><a href="#cite_note-23"><span class="cite-bracket">[</span>22<span class="cite-bracket">]</span></a></sup></figcaption></figure> <p>At first glance it may appear that the contestants of evolutionary games are the individuals present in each generation who directly participate in the game. But individuals live only through one game cycle, and instead it is the strategies that really contest with one another over the duration of these many-generation games. So it is ultimately genes that play out a full contest – selfish genes of strategy. The contesting genes are present in an individual and to a degree in all of the individual's kin. This can sometimes profoundly affect which strategies survive, especially with issues of cooperation and defection. <a href="/wiki/W._D._Hamilton" title="W. D. Hamilton">William Hamilton</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> known for his theory of <a href="/wiki/Kin_selection" title="Kin selection">kin selection</a>, explored many of these cases using game-theoretic models. Kin-related treatment of game contests<sup id="cite_ref-Brembs_25-0" class="reference"><a href="#cite_note-Brembs-25"><span class="cite-bracket">[</span>24<span class="cite-bracket">]</span></a></sup> helps to explain many aspects of the behaviour of <a href="/wiki/Social_insects" class="mw-redirect" title="Social insects">social insects</a>, the altruistic behaviour in parent-offspring interactions, mutual protection behaviours, and co-operative <a href="/wiki/Parental_care" title="Parental care">care of offspring</a>. For such games, Hamilton defined an extended form of fitness – <i><a href="/wiki/Inclusive_fitness" title="Inclusive fitness">inclusive fitness</a></i>, which includes an individual's offspring as well as any offspring equivalents found in kin. </p> <table class="wikitable"> <tbody><tr> <th>The mathematics of kin selection </th></tr> <tr> <td>The concept of <i>kin selection</i> is that: <dl><dd><i>inclusive fitness=own contribution to fitness + contribution of all relatives</i>.</dd></dl> <p>Fitness is measured relative to the average population; for example, fitness=1 means growth at the average rate for the population, fitness < 1 means having a decreasing share in the population (dying out), fitness > 1 means an increasing share in the population (taking over). </p><p>The inclusive fitness of an individual <b>w<sub>i</sub></b> is the sum of its specific fitness of itself <b>a<sub>i</sub></b> plus the specific fitness of each and every relative weighted by the degree of relatedness which equates to the <i>summation</i> of all <b>r<sub>j</sub>*b<sub>j</sub></b>....... where <b>r<sub>j</sub></b> is relatedness of a specific relative and <b>b<sub>j</sub></b> is that specific relative's fitness – producing: </p> <dl><dd><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 w_{i}=a_{i}+\sum _{j}r_{j}b_{j}.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>w</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mo>=</mo> <msub> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mo>+</mo> <munder> <mo>∑</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>j</mi> </mrow> </munder> <msub> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>j</mi> </mrow> </msub> <msub> <mi>b</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>j</mi> </mrow> </msub> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle w_{i}=a_{i}+\sum _{j}r_{j}b_{j}.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9ef32b2d5c0f1d54e8c895ef509d0379149e6108" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.338ex; width:18.687ex; height:5.843ex;" alt="{\displaystyle w_{i}=a_{i}+\sum _{j}r_{j}b_{j}.}"></span></dd></dl> <p>If individual a<sub>i</sub> sacrifices their "own average equivalent fitness of 1" by accepting a fitness cost C, and then to "get that loss back", w<sub>i</sub> must still be 1 (or greater than 1)...and using <b>R*B</b> to represent the summation results in: </p> <dl><dd><big><i><b>1< (1-C)+RB</b></i></big> ....or rearranging..... <big><i><b>R>C/B</b></i>.</big><sup id="cite_ref-Brembs_25-1" class="reference"><a href="#cite_note-Brembs-25"><span class="cite-bracket">[</span>24<span class="cite-bracket">]</span></a></sup></dd></dl> </td></tr></tbody></table> <p>Hamilton went beyond kin relatedness to work with <a href="/wiki/Robert_Axelrod_(political_scientist)" title="Robert Axelrod (political scientist)">Robert Axelrod</a>, analysing games of co-operation under conditions not involving kin where <a href="/wiki/Reciprocal_altruism" title="Reciprocal altruism">reciprocal altruism</a> came into play.<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> <div class="mw-heading mw-heading3"><h3 id="Eusociality_and_kin_selection">Eusociality and kin selection</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Evolutionary_game_theory&action=edit&section=12" title="Edit section: Eusociality and kin selection"><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:Meat_eater_ant_feeding_on_honey.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/e/eb/Meat_eater_ant_feeding_on_honey.jpg/220px-Meat_eater_ant_feeding_on_honey.jpg" decoding="async" width="220" height="147" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/e/eb/Meat_eater_ant_feeding_on_honey.jpg/330px-Meat_eater_ant_feeding_on_honey.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/e/eb/Meat_eater_ant_feeding_on_honey.jpg/440px-Meat_eater_ant_feeding_on_honey.jpg 2x" data-file-width="1600" data-file-height="1067" /></a><figcaption><a href="/wiki/Iridomyrmex_purpureus" class="mw-redirect" title="Iridomyrmex purpureus">Meat ant</a> workers (always female) are related to a parent by a factor of 0.5, to a sister by 0.75, to a child by 0.5 and to a brother by 0.25. Therefore, it is significantly more advantageous to help produce a sister (0.75) than to have a child (0.5).</figcaption></figure> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Eusociality" title="Eusociality">Eusociality</a></div> <p><a href="/wiki/Eusocial" class="mw-redirect" title="Eusocial">Eusocial</a> insect workers forfeit reproductive rights to their queen. It has been suggested that kin selection, based on the genetic makeup of these workers, may predispose them to altruistic behaviours.<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> Most eusocial insect societies have <a href="/wiki/Haplodiploid" class="mw-redirect" title="Haplodiploid">haplodiploid</a> sexual determination, which means that workers are unusually closely related.<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> </p><p>This explanation of insect eusociality has, however, been challenged by a few highly-noted evolutionary game theorists (Nowak and Wilson)<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> who have published a controversial alternative game theoretic explanation based on a sequential development and group selection effects proposed for these insect species.<sup id="cite_ref-30" class="reference"><a href="#cite_note-30"><span class="cite-bracket">[</span>29<span class="cite-bracket">]</span></a></sup> </p> <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=Evolutionary_game_theory&action=edit&section=13" 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> <p>A difficulty of the theory of evolution, recognised by Darwin himself, was the problem of <a href="/wiki/Altruism" title="Altruism">altruism</a>. If the basis for selection is at an individual level, altruism makes no sense at all. But universal selection at the group level (for the good of the species, not the individual) fails to pass the test of the mathematics of game theory and is certainly not the general case in nature.<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> Yet in many social animals, altruistic behaviour exists. The solution to this problem can be found in the application of evolutionary game theory to the <a href="/wiki/Prisoner%27s_dilemma" title="Prisoner's dilemma">prisoner's dilemma</a> game – a game which tests the payoffs of cooperating or in defecting from cooperation. It is the most studied game in all of game theory.<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><p>The analysis of the prisoner's dilemma is as a repetitive game. This affords competitors the possibility of retaliating for defection in previous rounds of the game. Many strategies have been tested; the best competitive strategies are general cooperation, with a reserved retaliatory response if necessary.<sup id="cite_ref-33" class="reference"><a href="#cite_note-33"><span class="cite-bracket">[</span>32<span class="cite-bracket">]</span></a></sup> The most famous and one of the most successful of these is <a href="/wiki/Tit-for-tat" class="mw-redirect" title="Tit-for-tat">tit-for-tat</a> with a simple algorithm. </p> <div class="mw-highlight mw-highlight-lang-python mw-content-ltr" dir="ltr"><pre><span></span><span class="k">def</span> <span class="nf">tit_for_tat</span><span class="p">(</span><span class="n">last_move_by_opponent</span><span class="p">):</span> <span class="w"> </span><span class="sd">"""Defect if opponent defects, else cooperate."""</span> <span class="k">if</span> <span class="n">last_move_by_opponent</span> <span class="o">==</span> <span class="n">defect</span><span class="p">:</span> <span class="n">defect</span><span class="p">()</span> <span class="k">else</span><span class="p">:</span> <span class="n">cooperate</span><span class="p">()</span> </pre></div> <p>The pay-off for any single round of the game is defined by the pay-off matrix for a single round game (shown in bar chart 1 below). In multi-round games the different choices – co-operate or defect – can be made in any particular round, resulting in a certain round payoff. It is, however, the possible accumulated pay-offs over the multiple rounds that count in shaping the overall pay-offs for differing multi-round strategies such as tit-for-tat. </p> <figure typeof="mw:File/Thumb"><a href="/wiki/File:PrisonersPayoff.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/3/31/PrisonersPayoff.jpg/400px-PrisonersPayoff.jpg" decoding="async" width="400" height="208" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/3/31/PrisonersPayoff.jpg/600px-PrisonersPayoff.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/3/31/PrisonersPayoff.jpg/800px-PrisonersPayoff.jpg 2x" data-file-width="1474" data-file-height="767" /></a><figcaption>Payoffs in two varieties of prisoner's dilemma game <br />Prisoner's dilemma: co-operate or defect <br />Payoff <sub>(temptation in defecting vs. co-operation)</sub> > Payoff <sub>(mutual co-operation)</sub> > Payoff<sub>(joint defection)</sub> > Payoff<sub>(sucker co-operates but opponent defects)</sub></figcaption></figure> <p>Example 1: The straightforward single round prisoner's dilemma game. The classic prisoner's dilemma game payoffs gives a player a maximum payoff if they defect and their partner co-operates (this choice is known as <i>temptation</i>). If, however, the player co-operates and their partner defects, they get the worst possible result (the suckers payoff). In these payoff conditions the best choice (a <a href="/wiki/Nash_equilibrium" title="Nash equilibrium">Nash equilibrium</a>) is to defect. </p><p>Example 2: Prisoner's dilemma played repeatedly. The strategy employed is <i>tit-for-tat</i> which alters behaviours based on the action taken by a partner in the previous round – i.e. reward co-operation and punish defection. The effect of this strategy in accumulated payoff over many rounds is to produce a higher payoff for both players' co-operation and a lower payoff for defection. This removes the temptation to defect. The suckers payoff also becomes less, although "invasion" by a pure defection strategy is not entirely eliminated. </p> <div class="mw-heading mw-heading3"><h3 id="Routes_to_altruism">Routes to altruism</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Evolutionary_game_theory&action=edit&section=14" title="Edit section: Routes to altruism"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Altruism takes place when one individual, at a cost (C) to itself, exercises a strategy that provides a benefit (B) to another individual. The cost may consist of a loss of capability or resource which helps in the battle for survival and reproduction, or an added risk to its own survival. Altruism strategies can arise through: </p> <table class="wikitable"> <tbody><tr> <th>Type</th> <th>Applies to:</th> <th>Situation</th> <th>Mathematical effect </th></tr> <tr valign="top"> <td><b>Kin selection</b> – (inclusive fitness of related contestants)</td> <td>Kin – genetically related individuals</td> <td>Evolutionary game participants are genes of strategy. The best payoff for an individual is not necessarily the best payoff for the gene. In any generation the player gene is <i>not</i> only in one individual, it is in a kin-group. The highest fitness payoff for the kin group is selected by natural selection. Therefore, strategies that include self-sacrifice on the part of individuals are often game winners – the evolutionarily stable strategy. Animals must live in kin-groups during part of the game for the opportunity for this altruistic sacrifice ever to take place.</td> <td>Games must take into account inclusive fitness. Fitness function is the combined fitness of a group of related contestants – each weighted by the degree of relatedness – relative to the total genetic population. The mathematical analysis of this gene-centric view of the game leads to Hamilton's rule, that the relatedness of the altruistic donor must exceed the cost-benefit ratio of the altruistic act itself:<sup id="cite_ref-Nowak_&_Sigmund_34-0" class="reference"><a href="#cite_note-Nowak_&_Sigmund-34"><span class="cite-bracket">[</span>33<span class="cite-bracket">]</span></a></sup> <dl><dd><i>R>c/b</i> R is relatedness, c the cost, b the benefit</dd></dl> </td></tr> <tr valign="top"> <td><b>Direct reciprocity</b></td> <td>Contestants that trade favours in paired relationships</td> <td>A game theoretic embodiment of "I'll scratch your back if you scratch mine". A pair of individuals exchange favours in a multi-round game. The individuals are recognisable to one another as partnered. The term "direct" applies because the return favour is specifically given back to the pair partner only.</td> <td>The characteristics of the multi-round game produce a danger of defection and the potentially lesser payoffs of cooperation in each round, but any such defection can lead to punishment in a following round – establishing the game as a repeated prisoner's dilemma. Therefore, the family of tit-for-tat strategies come to the fore.<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> </td></tr> <tr valign="top"> <td><b>Indirect reciprocity</b></td> <td>Related or non related contestants trade favours but without partnering. A return favour is "implied" but with no specific identified source who is to give it.</td> <td>The return favour is not derived from any particular established partner. The potential for indirect reciprocity exists for a specific organism if it lives in a cluster of individuals who can interact over an extended period of time. <p>It has been argued that human behaviours in establishing moral systems as well as the expending of significant energies in human society for tracking individual reputations is a direct effect of societies' reliance on strategies of indirect reciprocation.<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> </td> <td>The game is highly susceptible to defection, as direct retaliation is impossible. Therefore, indirect reciprocity will not work without keeping a social score, a measure of past co-operative behaviour. The mathematics lead to a modified version of Hamilton's rule where: <dl><dd><i>q>c/b</i> where q (the probability of knowing the social score) must be greater than the cost benefit ratio<sup id="cite_ref-37" class="reference"><a href="#cite_note-37"><span class="cite-bracket">[</span>36<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-38" class="reference"><a href="#cite_note-38"><span class="cite-bracket">[</span>37<span class="cite-bracket">]</span></a></sup></dd></dl> <p>Organisms that use social score are termed Discriminators, and require a higher level of cognition than strategies of simple direct reciprocity. As evolutionary biologist David Haig put it – "For direct reciprocity you need a face; for indirect reciprocity you need a name". </p> </td></tr></tbody></table> <div class="mw-heading mw-heading3"><h3 id="The_evolutionarily_stable_strategy">The evolutionarily stable strategy</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Evolutionary_game_theory&action=edit&section=15" title="Edit section: The evolutionarily stable strategy"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure typeof="mw:File/Thumb"><a href="/wiki/File:AssessorGraph.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/1/1e/AssessorGraph.jpg/300px-AssessorGraph.jpg" decoding="async" width="300" height="149" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/1/1e/AssessorGraph.jpg/450px-AssessorGraph.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/1/1e/AssessorGraph.jpg/600px-AssessorGraph.jpg 2x" data-file-width="1169" data-file-height="582" /></a><figcaption> The payoff matrix for the hawk dove game, with the addition of the assessor strategy. This "studies its opponent", behaving as a hawk when matched with an opponent it judges "weaker", like a dove when the opponent seems bigger and stronger. Assessor is an ESS, since it can invade both hawk and dove populations, and can withstand invasion by either hawk or dove mutants.</figcaption></figure> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Evolutionarily_Stable_Strategy" class="mw-redirect" title="Evolutionarily Stable Strategy">Evolutionarily Stable Strategy</a></div> <p>The <a href="/wiki/Evolutionarily_stable_strategy" title="Evolutionarily stable strategy">evolutionarily stable strategy</a> (ESS) is akin to the Nash equilibrium in classical game theory, but with mathematically extended criteria. Nash equilibrium is a game equilibrium where it is not rational for any player to deviate from their present strategy, provided that the others adhere to their strategies. An ESS is a state of game dynamics where, in a very large population of competitors, another mutant strategy cannot successfully enter the population to disturb the existing dynamic (which itself depends on the population mix). Therefore, a successful strategy (with an ESS) must be both effective against competitors when it is rare – to enter the previous competing population, and successful when later in high proportion in the population – to defend itself. This in turn means that the strategy must be successful when it contends with others exactly like itself.<sup id="cite_ref-39" class="reference"><a href="#cite_note-39"><span class="cite-bracket">[</span>38<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-40" class="reference"><a href="#cite_note-40"><span class="cite-bracket">[</span>39<span class="cite-bracket">]</span></a></sup><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>An ESS is not: </p> <ul><li>An optimal strategy: that would maximize fitness, and many ESS states are far below the maximum fitness achievable in a fitness landscape. (See hawk dove graph above as an example of this.)</li> <li>A singular solution: often several ESS conditions can exist in a competitive situation. A particular contest might stabilize into any one of these possibilities, but later a major perturbation in conditions can move the solution into one of the alternative ESS states.</li> <li>Always present: it is possible for there to be no ESS. An evolutionary game with no ESS is "rock-scissors-paper", as found in species such as the side-blotched lizard (<i><a href="/wiki/Uta_stansburiana" class="mw-redirect" title="Uta stansburiana">Uta stansburiana</a></i>).</li> <li>An unbeatable strategy: the ESS is only an uninvadeable strategy.</li></ul> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Agelenopsis_actuosa_fem_sp.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/8/88/Agelenopsis_actuosa_fem_sp.jpg/220px-Agelenopsis_actuosa_fem_sp.jpg" decoding="async" width="220" height="171" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/8/88/Agelenopsis_actuosa_fem_sp.jpg/330px-Agelenopsis_actuosa_fem_sp.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/8/88/Agelenopsis_actuosa_fem_sp.jpg/440px-Agelenopsis_actuosa_fem_sp.jpg 2x" data-file-width="800" data-file-height="621" /></a><figcaption>Female funnel web spiders (Agelenopsis aperta) contest with one another for the possession of their desert spider webs using the assessor strategy.<sup id="cite_ref-42" class="reference"><a href="#cite_note-42"><span class="cite-bracket">[</span>41<span class="cite-bracket">]</span></a></sup></figcaption></figure> <p>The ESS state can be solved for by exploring either the dynamics of population change to determine an ESS, or by solving equations for the stable stationary point conditions which define an ESS.<sup id="cite_ref-43" class="reference"><a href="#cite_note-43"><span class="cite-bracket">[</span>42<span class="cite-bracket">]</span></a></sup> For example, in the hawk dove game we can look for whether there is a static population mix condition where the fitness of doves will be exactly the same as fitness of hawks (therefore both having equivalent growth rates – a static point). </p><p>Let the chance of meeting a hawk=p so therefore the chance of meeting a dove is (1-p) </p><p>Let Whawk equal the payoff for hawk... </p><p>Whawk=payoff in the chance of meeting a dove + payoff in the chance of meeting a hawk </p><p>Taking the payoff matrix results and plugging them into the above equation: </p><p><span class="texhtml"><var>Whawk</var>= <var>V·(1-p)+(V/2-C/2)·p</var></span> </p><p>Similarly for a dove: </p><p><span class="texhtml"><var>Wdove</var>= <var>V/2·(1-p)+0·(p)</var></span> </p><p>so.... </p><p><span class="texhtml"><var>Wdove</var>= <var> V/2·(1-p) </var></span> </p><p>Equating the two fitnesses, hawk and dove </p><p><span class="texhtml"><var>V·(1-p)+(V/2-C/2)·p</var>= <var> V/2·(1-p) </var></span> </p><p>... and solving for p </p><p><span class="texhtml"><var>p</var>= <var>V/C</var></span> </p><p>so for this "static point" where the <i>population percent</i> is an ESS solves to be ESS<sub>(percent Hawk)</sub>=<i>V/C</i> </p><p>Similarly, using inequalities, it can be shown that an additional hawk or dove mutant entering this ESS state eventually results in less fitness for their kind – both a true Nash and an ESS equilibrium. This example shows that when the risks of contest injury or death (the cost C) is significantly greater than the potential reward (the benefit value V), the stable population will be mixed between aggressors and doves, and the proportion of doves will exceed that of the aggressors. This explains behaviours observed in nature. </p> <div class="mw-heading mw-heading2"><h2 id="Unstable_games,_cyclic_patterns"><span id="Unstable_games.2C_cyclic_patterns"></span>Unstable games, cyclic patterns</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Evolutionary_game_theory&action=edit&section=16" title="Edit section: Unstable games, cyclic patterns"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="Rock_paper_scissors">Rock paper scissors</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Evolutionary_game_theory&action=edit&section=17" title="Edit section: Rock paper scissors"><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:Rock_paper_scissors.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/e/e6/Rock_paper_scissors.jpg/220px-Rock_paper_scissors.jpg" decoding="async" width="220" height="176" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/e/e6/Rock_paper_scissors.jpg/330px-Rock_paper_scissors.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/e/e6/Rock_paper_scissors.jpg/440px-Rock_paper_scissors.jpg 2x" data-file-width="500" data-file-height="400" /></a><figcaption>Rock paper scissors</figcaption></figure> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:RockPaperMatrix.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/3/38/RockPaperMatrix.jpg/220px-RockPaperMatrix.jpg" decoding="async" width="220" height="165" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/3/38/RockPaperMatrix.jpg/330px-RockPaperMatrix.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/3/38/RockPaperMatrix.jpg/440px-RockPaperMatrix.jpg 2x" data-file-width="960" data-file-height="720" /></a><figcaption>Mutant invasion for rock paper scissors payoff matrix – an endless cycle</figcaption></figure> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Rock_paper_scissors" title="Rock paper scissors">Rock paper scissors</a></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:RPS_dynamics.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/7/7e/RPS_dynamics.jpg/220px-RPS_dynamics.jpg" decoding="async" width="220" height="144" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/7/7e/RPS_dynamics.jpg/330px-RPS_dynamics.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/7/7e/RPS_dynamics.jpg/440px-RPS_dynamics.jpg 2x" data-file-width="1134" data-file-height="741" /></a><figcaption>A computer simulation of the rock scissors paper game. The associated <a href="/wiki/Normal-form_game" title="Normal-form game">RPS game payoff matrix</a> is shown. Starting with an arbitrary population the percentage of the three morphs builds up into a continuously cycling pattern.</figcaption></figure> <p>Rock paper scissors incorporated into an evolutionary game has been used for modelling natural processes in the study of <a href="/wiki/Ecology" title="Ecology">ecology</a>.<sup id="cite_ref-44" class="reference"><a href="#cite_note-44"><span class="cite-bracket">[</span>43<span class="cite-bracket">]</span></a></sup> Using <a href="/wiki/Experimental_economics" title="Experimental economics">experimental economics</a> methods, scientists have used RPS games to test human social evolutionary dynamical behaviours in laboratories. The social cyclic behaviours, predicted by evolutionary game theory, have been observed in various laboratory experiments.<sup id="cite_ref-45" class="reference"><a href="#cite_note-45"><span class="cite-bracket">[</span>44<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-46" class="reference"><a href="#cite_note-46"><span class="cite-bracket">[</span>45<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Side-blotched_lizard_plays_the_RPS,_and_other_cyclical_games"><span id="Side-blotched_lizard_plays_the_RPS.2C_and_other_cyclical_games"></span>Side-blotched lizard plays the RPS, and other cyclical games</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Evolutionary_game_theory&action=edit&section=18" title="Edit section: Side-blotched lizard plays the RPS, and other cyclical games"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The first example of RPS in nature was seen in the behaviours and throat colours of a small lizard of western North America. The <a href="/wiki/Side-blotched_lizard" title="Side-blotched lizard">side-blotched lizard</a> (<i>Uta stansburiana</i>) is <a href="/wiki/Polymorphism_(biology)" title="Polymorphism (biology)">polymorphic</a> with three throat-colour morphs<sup id="cite_ref-47" class="reference"><a href="#cite_note-47"><span class="cite-bracket">[</span>46<span class="cite-bracket">]</span></a></sup> that each pursue a different mating strategy: </p> <figure class="mw-default-size mw-halign-left" typeof="mw:File/Thumb"><a href="/wiki/File:SideblotchedLizard.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/e/e5/SideblotchedLizard.jpg/220px-SideblotchedLizard.jpg" decoding="async" width="220" height="183" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/e/e5/SideblotchedLizard.jpg/330px-SideblotchedLizard.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/e/e5/SideblotchedLizard.jpg/440px-SideblotchedLizard.jpg 2x" data-file-width="933" data-file-height="777" /></a><figcaption>The <a href="/wiki/Side-blotched_lizard" title="Side-blotched lizard">side-blotched lizard</a> effectively uses a rock-paper-scissors mating strategy</figcaption></figure> <ul><li>The orange throat is very aggressive and operates over a large territory – attempting to mate with numerous females</li> <li>The unaggressive yellow throat mimics the markings and behavior of female lizards, and "sneakily" slips into the orange throat's territory to mate with the females there (thereby taking over the population)</li> <li>The blue throat mates with, and carefully guards, one female – making it impossible for the sneakers to succeed and therefore overtakes their place in a population</li></ul> <p>However the blue throats cannot overcome the more aggressive orange throats. Later work showed that the blue males are altruistic to other blue males, with three key traits: they signal with blue color, they recognize and settle next to other (unrelated) blue males, and they will even defend their partner against orange, to the death. This is the hallmark of another game of cooperation that involves a <a href="/wiki/Green-beard_effect" title="Green-beard effect">green-beard effect</a>.<sup id="cite_ref-48" class="reference"><a href="#cite_note-48"><span class="cite-bracket">[</span>47<span class="cite-bracket">]</span></a></sup><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> </p><p>The females in the same population have the same throat colours, and this affects how many offspring they produce and the size of the progeny, which generates cycles in density, yet another game – the <i>r-K</i> game.<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> Here, <i>r</i> is the <a href="/wiki/Malthusian_growth_model" title="Malthusian growth model">Malthusian parameter</a> governing exponential growth, and <i>K</i> is the <a href="/wiki/Carrying_capacity" title="Carrying capacity">carrying capacity of the environment</a>. Orange females have larger <a href="/wiki/Clutch_(eggs)" title="Clutch (eggs)">clutches</a> and smaller offspring which do well at low density. Yellow & blue females have smaller clutches and larger offspring which do well at high density. This generates perpetual cycles tightly tied to population density. The idea of cycles due to density regulation of two strategies originated with rodent researcher <a href="/wiki/Dennis_Chitty" title="Dennis Chitty">Dennis Chitty</a>, ergo these kinds of games lead to "Chitty cycles". There are games within games within games embedded in natural populations. These drive RPS cycles in the males with a periodicity of four years and <i>r-K</i> cycles in females with a two year period. </p><p>The overall situation corresponds to the rock, scissors, paper game, creating a four-year population cycle. The RPS game in male side-blotched lizards does not have an ESS, but it has a Nash equilibrium (NE) with endless orbits around the <a href="/wiki/Fixed_point_(mathematics)#Attracting_fixed_points" title="Fixed point (mathematics)">NE attractor</a>. Following this Side-blotched lizard research, many other three-strategy polymorphisms have been discovered in lizards and some of these have RPS dynamics merging the male game and density regulation game in a single sex (males).<sup id="cite_ref-51" class="reference"><a href="#cite_note-51"><span class="cite-bracket">[</span>50<span class="cite-bracket">]</span></a></sup> More recently, mammals have been shown to harbour the same RPS game in males and <i>r-K</i> game in females, with coat-colour polymorphisms and behaviours that drive cycles.<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> This game is also linked to the evolution of male care in rodents, and monogamy, and drives <a href="/wiki/Speciation#Rates" title="Speciation">speciation rates</a>. There are <i>r-K</i> strategy games linked to rodent population cycles (and lizard cycles).<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> </p><p>When he read that these lizards were essentially engaged in a game with a rock-paper-scissors structure, John Maynard Smith is said to have exclaimed "They have read my book!".<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> </p> <div class="mw-heading mw-heading2"><h2 id="Signalling,_sexual_selection_and_the_handicap_principle"><span id="Signalling.2C_sexual_selection_and_the_handicap_principle"></span>Signalling, sexual selection and the handicap principle</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Evolutionary_game_theory&action=edit&section=19" title="Edit section: Signalling, sexual selection and the handicap principle"><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:Peacock_at_Warwick_Castle.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/b/b1/Peacock_at_Warwick_Castle.jpg/220px-Peacock_at_Warwick_Castle.jpg" decoding="async" width="220" height="165" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/b/b1/Peacock_at_Warwick_Castle.jpg/330px-Peacock_at_Warwick_Castle.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/b/b1/Peacock_at_Warwick_Castle.jpg/440px-Peacock_at_Warwick_Castle.jpg 2x" data-file-width="4000" data-file-height="3000" /></a><figcaption>The peacock's tail may be an instance of the <a href="/wiki/Handicap_principle" title="Handicap principle">handicap principle</a> in action</figcaption></figure> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Signalling_theory" title="Signalling theory">Signalling theory</a></div> <p>Aside from the difficulty of explaining how altruism exists in many evolved organisms, Darwin was also bothered by a second conundrum – why a significant number of species have phenotypical attributes that are patently disadvantageous to them with respect to their survival – and should by the process of natural section be selected against – e.g. the massive inconvenient feather structure found in a peacock's tail. Regarding this issue Darwin wrote to a colleague "The sight of a feather in a peacock's tail, whenever I gaze at it, makes me sick."<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> It is the mathematics of evolutionary game theory, which has not only explained the existence of altruism, but also explains the totally counterintuitive existence of the peacock's tail and other such biological encumbrances. </p><p>On analysis, problems of biological life are not at all unlike the problems that define economics – eating (akin to resource acquisition and management), survival (competitive strategy) and reproduction (investment, risk and return). Game theory was originally conceived as a mathematical analysis of economic processes and indeed this is why it has proven so useful in explaining so many biological behaviours. One important further refinement of the evolutionary game theory model that has economic overtones rests on the analysis of costs. A simple model of cost assumes that all competitors suffer the same penalty imposed by the game costs, but this is not the case. More successful players will be endowed with or will have accumulated a higher "wealth reserve" or "affordability" than less-successful players. This wealth effect in evolutionary game theory is represented mathematically by "<a href="/wiki/Resource_holding_potential" title="Resource holding potential">resource holding potential</a> (RHP)" and shows that the effective cost to a competitor with a higher RHP are not as great as for a competitor with a lower RHP. As a higher RHP individual is a more desirable mate in producing potentially successful offspring, it is only logical that with sexual selection RHP should have evolved to be signalled in some way by the competing rivals, and for this to work this signalling must be done <i>honestly</i>. <a href="/wiki/Amotz_Zahavi" title="Amotz Zahavi">Amotz Zahavi</a> has developed this thinking in what is known as the "<a href="/wiki/Handicap_principle" title="Handicap principle">handicap principle</a>",<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> where superior competitors signal their superiority by a costly display. As higher RHP individuals can properly afford such a costly display this signalling is inherently honest, and can be taken as such by the signal receiver. In nature this is illustrated than in the costly plumage of the <a href="/wiki/Peacock" class="mw-redirect" title="Peacock">peacock</a>. The mathematical proof of the handicap principle was developed by <a href="/wiki/Alan_Grafen" title="Alan Grafen">Alan Grafen</a> using evolutionary game-theoretic modelling.<sup id="cite_ref-Grafen_1990_517–546_57-0" class="reference"><a href="#cite_note-Grafen_1990_517–546-57"><span class="cite-bracket">[</span>56<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Coevolution">Coevolution</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Evolutionary_game_theory&action=edit&section=20" title="Edit section: Coevolution"><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/Coevolution" title="Coevolution">Coevolution</a></div> <p>Two types of dynamics: </p> <ul><li>Evolutionary games which lead to a stable situation or point of stasis for contending strategies which result in an evolutionarily stable strategy</li> <li>Evolutionary games which exhibit a cyclic behaviour (as with RPS game) where the proportions of contending strategies continuously cycle over time within the overall population</li></ul> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1237032888/mw-parser-output/.tmulti"><div class="thumb tmulti tright"><div class="thumbinner multiimageinner" style="width:368px;max-width:368px"><div class="trow"><div class="tsingle" style="width:182px;max-width:182px"><div class="thumbimage"><span typeof="mw:File"><a href="/wiki/File:NHM_Taricha_granulosa_cropped.jpg" class="mw-file-description"><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/f/f1/NHM_Taricha_granulosa_cropped.jpg/180px-NHM_Taricha_granulosa_cropped.jpg" decoding="async" width="180" height="244" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/f/f1/NHM_Taricha_granulosa_cropped.jpg/270px-NHM_Taricha_granulosa_cropped.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/f/f1/NHM_Taricha_granulosa_cropped.jpg/360px-NHM_Taricha_granulosa_cropped.jpg 2x" data-file-width="398" data-file-height="540" /></a></span></div><div class="thumbcaption">Competitive Coevolution – The <a href="/wiki/Rough-skinned_newt" title="Rough-skinned newt">rough-skinned newt</a> (<i>Tarricha granulosa</i>) is highly toxic, due to an <a href="/wiki/Evolutionary_arms_race" title="Evolutionary arms race">evolutionary arms race</a> with a predator, the <a href="/wiki/Common_garter_snake" title="Common garter snake">common garter snake</a> (<i>Thamnophis sirtalis</i>), which in turn is highly tolerant of the poison. The two are locked in a <a href="/wiki/Red_Queen%27s_Hypothesis" class="mw-redirect" title="Red Queen's Hypothesis">Red Queen</a> arms race.<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></div></div><div class="tsingle" style="width:182px;max-width:182px"><div class="thumbimage"><span typeof="mw:File"><a href="/wiki/File:NHM_Xanthopan_morgani.jpg" class="mw-file-description"><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/9/9d/NHM_Xanthopan_morgani.jpg/180px-NHM_Xanthopan_morgani.jpg" decoding="async" width="180" height="245" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/9/9d/NHM_Xanthopan_morgani.jpg/270px-NHM_Xanthopan_morgani.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/9/9d/NHM_Xanthopan_morgani.jpg/360px-NHM_Xanthopan_morgani.jpg 2x" data-file-width="1080" data-file-height="1472" /></a></span></div><div class="thumbcaption">Mutualistic Coevolution – <a href="/wiki/Darwin%27s_orchid" class="mw-redirect" title="Darwin's orchid">Darwin's orchid</a> (<i>Angraecum sesquipedale</i>) and the moth <a href="/wiki/Morgan%27s_sphinx" class="mw-redirect" title="Morgan's sphinx">Morgan's sphinx</a> (<i>Xanthopan morgani</i>) have a mutual relationship where the moth gains pollen and the flower is <a href="/wiki/Pollination" title="Pollination">pollinated</a>.</div></div></div></div></div> <p>A third, <a href="/wiki/Coevolution" title="Coevolution">coevolutionary</a>, dynamic, combines intra-specific and inter-specific competition. Examples include predator-prey competition and host-parasite co-evolution, as well as mutualism. Evolutionary game models have been created for pairwise and multi-species coevolutionary systems.<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> The general dynamic differs between competitive systems and mutualistic systems. </p><p>In competitive (non-mutualistic) inter-species coevolutionary system the species are involved in an arms race – where adaptations that are better at competing against the other species tend to be preserved. Both game payoffs and replicator dynamics reflect this. This leads to a <a href="/wiki/Red_Queen%27s_Hypothesis" class="mw-redirect" title="Red Queen's Hypothesis">Red Queen</a> dynamic where the protagonists must "run as fast as they can to just stay in one place".<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> </p><p>A number of evolutionary game theory models have been produced to encompass coevolutionary situations. A key factor applicable in these coevolutionary systems is the continuous adaptation of strategy in such arms races. Coevolutionary modelling therefore often includes <a href="/wiki/Genetic_algorithm" title="Genetic algorithm">genetic algorithms</a> to reflect mutational effects, while computers simulate the dynamics of the overall coevolutionary game. The resulting dynamics are studied as various parameters are modified. Because several variables are simultaneously at play, solutions become the province of multi-variable optimisation. The mathematical criteria of determining stable points are <a href="/wiki/Pareto_efficiency" title="Pareto efficiency">Pareto efficiency</a> and Pareto dominance, a measure of solution optimality peaks in multivariable systems.<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> </p><p><a href="/wiki/Carl_Bergstrom" title="Carl Bergstrom">Carl Bergstrom</a> and Michael Lachmann apply evolutionary game theory to the division of benefits in <a href="/wiki/Mutualism_(biology)" title="Mutualism (biology)">mutualistic</a> interactions between organisms. Darwinian assumptions about fitness are modeled using replicator dynamics to show that the organism evolving at a slower rate in a mutualistic relationship gains a disproportionately high share of the benefits or payoffs.<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> </p> <div class="mw-heading mw-heading2"><h2 id="Extending_the_model">Extending the model</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Evolutionary_game_theory&action=edit&section=21" title="Edit section: Extending the model"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>A <a href="/wiki/Mathematical_model" title="Mathematical model">mathematical model</a> analysing the behaviour of a system needs initially to be as simple as possible to aid in developing a base understanding the fundamentals, or “first order effects”, pertaining to what is being studied. With this understanding in place it is then appropriate to see if other, more subtle, parameters (second order effects) further impact the primary behaviours or shape additional behaviours in the system. Following Maynard Smith's seminal work in evolutionary game theory, the subject has had a number of very significant extensions which have shed more light on understanding evolutionary dynamics, particularly in the area of altruistic behaviors. Some of these key extensions to evolutionary game theory are: </p> <figure typeof="mw:File/Thumb"><a href="/wiki/File:SpatialExamp.gif" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/e/e8/SpatialExamp.gif/150px-SpatialExamp.gif" decoding="async" width="150" height="113" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/e/e8/SpatialExamp.gif/225px-SpatialExamp.gif 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/e/e8/SpatialExamp.gif/300px-SpatialExamp.gif 2x" data-file-width="960" data-file-height="720" /></a><figcaption><b> A Spatial Game</b><br />In a spatial evolutionary game contestants meet in contests at fixed grid positions and only interact with immediate neighbors. Shown here are the dynamics of a Hawk Dove contest, showing Hawk and Dove contestants as well as the changes of strategy taking place in the various cells</figcaption></figure> <div class="mw-heading mw-heading3"><h3 id="Spatial_games">Spatial games</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Evolutionary_game_theory&action=edit&section=22" title="Edit section: Spatial games"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Geographic factors in evolution include <a href="/wiki/Gene_flow" title="Gene flow">gene flow</a> and <a href="/wiki/Horizontal_gene_transfer" title="Horizontal gene transfer">horizontal gene transfer</a>. Spatial game models represent geometry by putting contestants in a lattice of cells: contests take place only with immediate neighbours. Winning strategies take over these immediate neighbourhoods and then interact with adjacent neighbourhoods. This model is useful in showing how pockets of co-operators can invade and introduce altruism in the Prisoners Dilemma game,<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> where Tit for Tat (TFT) is a Nash Equilibrium but NOT also an ESS. Spatial structure is sometimes abstracted into a general network of interactions.<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><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> This is the foundation of <a href="/wiki/Evolutionary_graph_theory" title="Evolutionary graph theory">evolutionary graph theory</a>. </p> <div class="mw-heading mw-heading3"><h3 id="Effects_of_having_information">Effects of having information</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Evolutionary_game_theory&action=edit&section=23" title="Edit section: Effects of having information"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>In evolutionary game theory as in conventional <a href="/wiki/Game_Theory" class="mw-redirect" title="Game Theory">Game Theory</a> the effect of Signalling (the acquisition of information) is of critical importance, as in Indirect Reciprocity in Prisoners Dilemma (where contests between the SAME paired individuals are NOT repetitive). This models the reality of most normal social interactions which are non-kin related. Unless a probability measure of reputation is available in Prisoners Dilemma only direct reciprocity can be achieved.<sup id="cite_ref-Nowak_&_Sigmund_34-1" class="reference"><a href="#cite_note-Nowak_&_Sigmund-34"><span class="cite-bracket">[</span>33<span class="cite-bracket">]</span></a></sup> With this information indirect reciprocity is also supported. </p><p>Alternatively, agents might have access to an arbitrary signal initially uncorrelated to strategy but becomes correlated due to evolutionary dynamics. This is the <a href="/wiki/Green-beard_effect" title="Green-beard effect">green-beard effect</a> (see side-blotched lizards, above) or evolution of ethnocentrism in humans.<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> Depending on the game, it can allow the evolution of either cooperation or irrational hostility.<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> </p><p>From molecular to multicellular level, a <a href="/wiki/Signaling_game" title="Signaling game">signaling game</a> model with information asymmetry between sender and receiver might be appropriate, such as in mate attraction<sup id="cite_ref-Grafen_1990_517–546_57-1" class="reference"><a href="#cite_note-Grafen_1990_517–546-57"><span class="cite-bracket">[</span>56<span class="cite-bracket">]</span></a></sup> or evolution of translation machinery from RNA strings.<sup id="cite_ref-68" class="reference"><a href="#cite_note-68"><span class="cite-bracket">[</span>67<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Finite_populations">Finite populations</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Evolutionary_game_theory&action=edit&section=24" title="Edit section: Finite populations"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Many evolutionary games have been modelled in finite populations to see the effect this may have, for example in the success of mixed strategies. </p> <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=Evolutionary_game_theory&action=edit&section=25" title="Edit section: See also"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1184024115">.mw-parser-output .div-col{margin-top:0.3em;column-width:30em}.mw-parser-output .div-col-small{font-size:90%}.mw-parser-output .div-col-rules{column-rule:1px solid #aaa}.mw-parser-output .div-col dl,.mw-parser-output .div-col ol,.mw-parser-output .div-col ul{margin-top:0}.mw-parser-output .div-col li,.mw-parser-output .div-col dd{page-break-inside:avoid;break-inside:avoid-column}</style><div class="div-col" style="column-width: 20em;"> <ul><li><a href="/wiki/Adaptive_dynamics" class="mw-redirect" title="Adaptive dynamics">Adaptive dynamics</a></li> <li><a href="/wiki/Behavioral_ecology" title="Behavioral ecology">Behavioral ecology</a></li> <li><a href="/wiki/Dynamical_systems" class="mw-redirect" title="Dynamical systems">Dynamical systems</a></li> <li><a href="/wiki/Evolutionary_dynamics" title="Evolutionary dynamics">Evolutionary dynamics</a></li> <li><a href="/wiki/Gene-centered_view_of_evolution" title="Gene-centered view of evolution">Gene-centered view of evolution</a></li> <li><a href="/wiki/Memetics" title="Memetics">Memetics</a></li></ul> </div> <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=Evolutionary_game_theory&action=edit&section=26" 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-18"><span class="mw-cite-backlink"><b><a href="#cite_ref-18">^</a></b></span> <span class="reference-text">Maynard Smith chose the name "hawk dove" from descriptions of political views current during the <a href="/wiki/Vietnam_War" title="Vietnam War">Vietnam War</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=Evolutionary_game_theory&action=edit&section=27" 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 reflist-columns references-column-width" style="column-width: 30em;"> <ol class="references"> <li id="cite_note-Price-1"><span class="mw-cite-backlink">^ <a href="#cite_ref-Price_1-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-Price_1-1"><sup><i><b>b</b></i></sup></a> <a href="#cite_ref-Price_1-2"><sup><i><b>c</b></i></sup></a> <a href="#cite_ref-Price_1-3"><sup><i><b>d</b></i></sup></a> <a href="#cite_ref-Price_1-4"><sup><i><b>e</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="CITEREFMaynard_SmithPrice1973" class="citation journal cs1">Maynard Smith, John; Price, G. R. (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+G.+R.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AEvolutionary+game+theory" class="Z3988"></span></span> </li> <li id="cite_note-Newton2018renaissance-2"><span class="mw-cite-backlink"><b><a href="#cite_ref-Newton2018renaissance_2-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFNewton2018" class="citation journal cs1">Newton, Jonathan (2018). <a rel="nofollow" class="external text" href="https://www.econstor.eu/bitstream/10419/179191/1/games-09-00031-v2.pdf">"Evolutionary Game Theory: A Renaissance"</a> <span class="cs1-format">(PDF)</span>. <i>Games</i>. <b>9</b> (2): 31. <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/10.3390%2Fg9020031">10.3390/g9020031</a></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Games&rft.atitle=Evolutionary+Game+Theory%3A+A+Renaissance&rft.volume=9&rft.issue=2&rft.pages=31&rft.date=2018&rft_id=info%3Adoi%2F10.3390%2Fg9020031&rft.aulast=Newton&rft.aufirst=Jonathan&rft_id=https%3A%2F%2Fwww.econstor.eu%2Fbitstream%2F10419%2F179191%2F1%2Fgames-09-00031-v2.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3AEvolutionary+game+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="CITEREFEasleyKleinberg2010" class="citation book cs1">Easley, David; Kleinberg, Jon (2010). <a rel="nofollow" class="external text" href="http://www.cs.cornell.edu/home/kleinber/networks-book/networks-book-ch07.pdf"><i>Networks, Crowds, and Markets: Reasoning About a Highly Connected World</i></a> <span class="cs1-format">(PDF)</span>. Cambridge University Press. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/9780521195331" title="Special:BookSources/9780521195331"><bdi>9780521195331</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Networks%2C+Crowds%2C+and+Markets%3A+Reasoning+About+a+Highly+Connected+World&rft.pub=Cambridge+University+Press&rft.date=2010&rft.isbn=9780521195331&rft.aulast=Easley&rft.aufirst=David&rft.au=Kleinberg%2C+Jon&rft_id=http%3A%2F%2Fwww.cs.cornell.edu%2Fhome%2Fkleinber%2Fnetworks-book%2Fnetworks-book-ch07.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3AEvolutionary+game+theory" class="Z3988"></span></span> </li> <li id="cite_note-4"><span class="mw-cite-backlink"><b><a href="#cite_ref-4">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFMichihiro1997" class="citation book cs1"><a href="/wiki/Michihiro_Kandori" title="Michihiro Kandori">Michihiro, Kandori</a> (1997). "Evolutionary game theory in economics". In Kreps, David M.; Wallis, Kenneth F. (eds.). <i>Advances in Economics and Econometrics : Theory and Applications</i>. Vol. 1. Cambridge University Press. pp. 243–277. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-521-58983-5" title="Special:BookSources/0-521-58983-5"><bdi>0-521-58983-5</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=Evolutionary+game+theory+in+economics&rft.btitle=Advances+in+Economics+and+Econometrics+%3A+Theory+and+Applications&rft.pages=243-277&rft.pub=Cambridge+University+Press&rft.date=1997&rft.isbn=0-521-58983-5&rft.aulast=Michihiro&rft.aufirst=Kandori&rfr_id=info%3Asid%2Fen.wikipedia.org%3AEvolutionary+game+theory" class="Z3988"></span></span> </li> <li id="cite_note-5"><span class="mw-cite-backlink"><b><a href="#cite_ref-5">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFNeumann1928" class="citation cs2">Neumann, J. v. (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=Neumann&rft.aufirst=J.+v.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AEvolutionary+game+theory" class="Z3988"></span> English translation: <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFTuckerLuce1959" class="citation cs2">Tucker, A. W.; Luce, R. D., eds. (1959), <a rel="nofollow" class="external text" href="https://books.google.com/books?id=9lSVFzsTGWsC&pg=PA13">"On the Theory of Games of Strategy"</a>, <i>Contributions to the Theory of Games</i>, vol. 4, Princeton University Press, pp. 13–42, <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0691079374" title="Special:BookSources/0691079374"><bdi>0691079374</bdi></a></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=On+the+Theory+of+Games+of+Strategy&rft.btitle=Contributions+to+the+Theory+of+Games&rft.pages=13-42&rft.pub=Princeton+University+Press&rft.date=1959&rft.isbn=0691079374&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3D9lSVFzsTGWsC%26pg%3DPA13&rfr_id=info%3Asid%2Fen.wikipedia.org%3AEvolutionary+game+theory" class="Z3988"></span></span> </li> <li id="cite_note-6"><span class="mw-cite-backlink"><b><a href="#cite_ref-6">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFMirowski1992" class="citation book cs1">Mirowski, Philip (1992). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=9CHY2Gozh1MC&pg=PA113">"What Were von Neumann and Morgenstern Trying to Accomplish?"</a>. 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%3AEvolutionary+game+theory" class="Z3988"></span></span> </li> <li id="cite_note-7"><span class="mw-cite-backlink"><b><a href="#cite_ref-7">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFCohen,_Marek2004" class="citation book cs1">Cohen, Marek (2004). <i>A Reason for Everything</i>. Faber and Faber. pp. 231–240. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-571-22393-0" title="Special:BookSources/978-0-571-22393-0"><bdi>978-0-571-22393-0</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=A+Reason+for+Everything&rft.pages=231-240&rft.pub=Faber+and+Faber&rft.date=2004&rft.isbn=978-0-571-22393-0&rft.au=Cohen%2C+Marek&rfr_id=info%3Asid%2Fen.wikipedia.org%3AEvolutionary+game+theory" class="Z3988"></span></span> </li> <li id="cite_note-8"><span class="mw-cite-backlink"><b><a href="#cite_ref-8">^</a></b></span> <span class="reference-text">Video Interview – John Maynard Smith – <a rel="nofollow" class="external text" href="http://www.webofstories.com/play/7294?o=MS">The creation of Evolutionary Game Theory</a></span> </li> <li id="cite_note-9"><span class="mw-cite-backlink"><b><a href="#cite_ref-9">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFVincent,_Thomas2005" class="citation book cs1">Vincent, Thomas (2005). <span class="id-lock-limited" title="Free access subject to limited trial, subscription normally required"><a rel="nofollow" class="external text" href="https://archive.org/details/evolutionarygame00tlvi"><i>Evolutionary Game Theory, Natural Selection, and Darwinian Dynamics</i></a></span>. Cambridge University Press. pp. <a rel="nofollow" class="external text" href="https://archive.org/details/evolutionarygame00tlvi/page/n90">72</a>–87. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-521-84170-2" title="Special:BookSources/978-0-521-84170-2"><bdi>978-0-521-84170-2</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Evolutionary+Game+Theory%2C+Natural+Selection%2C+and+Darwinian+Dynamics&rft.pages=72-87&rft.pub=Cambridge+University+Press&rft.date=2005&rft.isbn=978-0-521-84170-2&rft.au=Vincent%2C+Thomas&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Fevolutionarygame00tlvi&rfr_id=info%3Asid%2Fen.wikipedia.org%3AEvolutionary+game+theory" class="Z3988"></span></span> </li> <li id="cite_note-JMSbook-10"><span class="mw-cite-backlink"><b><a href="#cite_ref-JMSbook_10-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFMaynard_Smith1982" class="citation book cs1"><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>. 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(2010). <i>The Price of Altruism</i>. Bodley Head. pp. Chapter 9. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-1-847-92062-1" title="Special:BookSources/978-1-847-92062-1"><bdi>978-1-847-92062-1</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=The+Price+of+Altruism&rft.pages=Chapter+9&rft.pub=Bodley+Head&rft.date=2010&rft.isbn=978-1-847-92062-1&rft.au=Harman%2C+O.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AEvolutionary+game+theory" class="Z3988"></span></span> </li> <li id="cite_note-23"><span class="mw-cite-backlink"><b><a href="#cite_ref-23">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFDugatkin,_Alan2004" class="citation book cs1">Dugatkin, Alan (2004). <i>Principles of Animal Behavior</i>. 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"Mate selection – a selection for a handicap". <i>Journal of Theoretical Biology</i>. <b>53</b> (1): 205–214. <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/1975JThBi..53..205Z">1975JThBi..53..205Z</a>. <a href="/wiki/CiteSeerX_(identifier)" class="mw-redirect" title="CiteSeerX (identifier)">CiteSeerX</a> <span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.586.3819">10.1.1.586.3819</a></span>. <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%2F0022-5193%2875%2990111-3">10.1016/0022-5193(75)90111-3</a>. <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/1195756">1195756</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+Theoretical+Biology&rft.atitle=Mate+selection+%E2%80%93+a+selection+for+a+handicap&rft.volume=53&rft.issue=1&rft.pages=205-214&rft.date=1975&rft_id=https%3A%2F%2Fciteseerx.ist.psu.edu%2Fviewdoc%2Fsummary%3Fdoi%3D10.1.1.586.3819%23id-name%3DCiteSeerX&rft_id=info%3Apmid%2F1195756&rft_id=info%3Adoi%2F10.1016%2F0022-5193%2875%2990111-3&rft_id=info%3Abibcode%2F1975JThBi..53..205Z&rft.aulast=Zahavi&rft.aufirst=A.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AEvolutionary+game+theory" class="Z3988"></span></span> </li> <li id="cite_note-Grafen_1990_517–546-57"><span class="mw-cite-backlink">^ <a href="#cite_ref-Grafen_1990_517–546_57-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-Grafen_1990_517–546_57-1"><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="CITEREFGrafen1990" class="citation journal cs1"><a href="/wiki/Alan_Grafen" title="Alan Grafen">Grafen, A.</a> (1990). "Biological signals as handicaps". <i>Journal of Theoretical Biology</i>. <b>144</b> (4): 517–546. <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/1990JThBi.144..517G">1990JThBi.144..517G</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1016%2FS0022-5193%2805%2980088-8">10.1016/S0022-5193(05)80088-8</a>. <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/2402153">2402153</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+Theoretical+Biology&rft.atitle=Biological+signals+as+handicaps&rft.volume=144&rft.issue=4&rft.pages=517-546&rft.date=1990&rft_id=info%3Apmid%2F2402153&rft_id=info%3Adoi%2F10.1016%2FS0022-5193%2805%2980088-8&rft_id=info%3Abibcode%2F1990JThBi.144..517G&rft.aulast=Grafen&rft.aufirst=A.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AEvolutionary+game+theory" class="Z3988"></span></span> </li> <li id="cite_note-58"><span class="mw-cite-backlink"><b><a href="#cite_ref-58">^</a></b></span> <span class="reference-text">Pallen, M., <i>Rough Guide to Evolution</i>, Penguin Books, 2009, p.123, <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/978-1-85828-946-5" title="Special:BookSources/978-1-85828-946-5">978-1-85828-946-5</a></span> </li> <li id="cite_note-59"><span class="mw-cite-backlink"><b><a href="#cite_ref-59">^</a></b></span> <span class="reference-text">Matja, Szolnoki, "Coevolutionary games – a mini review", Biosystems, 2009</span> </li> <li id="cite_note-60"><span class="mw-cite-backlink"><b><a href="#cite_ref-60">^</a></b></span> <span class="reference-text">Cliff and Miller, "Tracking the red queen: Measurements of adaptive progress in co-evolutionary simulations", European Conference on Artificial Life, p. 200–218, 1995</span> </li> <li id="cite_note-61"><span class="mw-cite-backlink"><b><a href="#cite_ref-61">^</a></b></span> <span class="reference-text">Sevan, Ficici and Pollack, "Pareto optimality in coevolutionary learning", European Conference on Artificial Life, pp. 316–325, 2001</span> </li> <li id="cite_note-62"><span class="mw-cite-backlink"><b><a href="#cite_ref-62">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFBergstromLachmann2003" class="citation journal cs1">Bergstrom, C.; Lachmann, M. (2003). <a rel="nofollow" class="external text" href="https://www.ncbi.nlm.nih.gov/pmc/articles/PMC141041">"The red king effect: when the slowest runner wins the coevolutionary race"</a>. <i>Proceedings of the National Academy of Sciences</i>. <b>100</b> (2): 593–598. <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/2003PNAS..100..593B">2003PNAS..100..593B</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.0134966100">10.1073/pnas.0134966100</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/PMC141041">141041</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/12525707">12525707</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=The+red+king+effect%3A+when+the+slowest+runner+wins+the+coevolutionary+race&rft.volume=100&rft.issue=2&rft.pages=593-598&rft.date=2003&rft_id=https%3A%2F%2Fwww.ncbi.nlm.nih.gov%2Fpmc%2Farticles%2FPMC141041%23id-name%3DPMC&rft_id=info%3Apmid%2F12525707&rft_id=info%3Adoi%2F10.1073%2Fpnas.0134966100&rft_id=info%3Abibcode%2F2003PNAS..100..593B&rft.aulast=Bergstrom&rft.aufirst=C.&rft.au=Lachmann%2C+M.&rft_id=https%3A%2F%2Fwww.ncbi.nlm.nih.gov%2Fpmc%2Farticles%2FPMC141041&rfr_id=info%3Asid%2Fen.wikipedia.org%3AEvolutionary+game+theory" class="Z3988"></span></span> </li> <li id="cite_note-63"><span class="mw-cite-backlink"><b><a href="#cite_ref-63">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFNowak,_Martin2006" class="citation book cs1">Nowak, Martin (2006). <span class="id-lock-limited" title="Free access subject to limited trial, subscription normally required"><a rel="nofollow" class="external text" href="https://archive.org/details/evolutionarydyna00nowa_778"><i>Evolutionary Dynamics</i></a></span>. Harvard University Press. pp. <a rel="nofollow" class="external text" href="https://archive.org/details/evolutionarydyna00nowa_778/page/n165">152</a>–154. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-674-02338-3" title="Special:BookSources/978-0-674-02338-3"><bdi>978-0-674-02338-3</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Evolutionary+Dynamics&rft.pages=152-154&rft.pub=Harvard+University+Press&rft.date=2006&rft.isbn=978-0-674-02338-3&rft.au=Nowak%2C+Martin&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Fevolutionarydyna00nowa_778&rfr_id=info%3Asid%2Fen.wikipedia.org%3AEvolutionary+game+theory" class="Z3988"></span></span> </li> <li id="cite_note-64"><span class="mw-cite-backlink"><b><a href="#cite_ref-64">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFAlbertBarabasi2002" class="citation journal cs1">Albert, Reka; Barabasi, Albert-Laszlo (2002). <a rel="nofollow" class="external text" href="http://egtheory.wordpress.com/2012/03/21/spatial-structure/">"Statistical mechanics of complex networks"</a>. <i>Reviews of Modern Physics</i>. <b>74</b> (1): 47–97. <a href="/wiki/ArXiv_(identifier)" class="mw-redirect" title="ArXiv (identifier)">arXiv</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://arxiv.org/abs/cond-mat/0106096">cond-mat/0106096</a></span>. <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/2002RvMP...74...47A">2002RvMP...74...47A</a>. <a href="/wiki/CiteSeerX_(identifier)" class="mw-redirect" title="CiteSeerX (identifier)">CiteSeerX</a> <span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.242.4753">10.1.1.242.4753</a></span>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1103%2FRevModPhys.74.47">10.1103/RevModPhys.74.47</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:60545">60545</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Reviews+of+Modern+Physics&rft.atitle=Statistical+mechanics+of+complex+networks&rft.volume=74&rft.issue=1&rft.pages=47-97&rft.date=2002&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A60545%23id-name%3DS2CID&rft_id=info%3Abibcode%2F2002RvMP...74...47A&rft_id=https%3A%2F%2Fciteseerx.ist.psu.edu%2Fviewdoc%2Fsummary%3Fdoi%3D10.1.1.242.4753%23id-name%3DCiteSeerX&rft_id=info%3Adoi%2F10.1103%2FRevModPhys.74.47&rft_id=info%3Aarxiv%2Fcond-mat%2F0106096&rft.aulast=Albert&rft.aufirst=Reka&rft.au=Barabasi%2C+Albert-Laszlo&rft_id=http%3A%2F%2Fegtheory.wordpress.com%2F2012%2F03%2F21%2Fspatial-structure%2F&rfr_id=info%3Asid%2Fen.wikipedia.org%3AEvolutionary+game+theory" class="Z3988"></span></span> </li> <li id="cite_note-65"><span class="mw-cite-backlink"><b><a href="#cite_ref-65">^</a></b></span> <span class="reference-text">H. Tembine, E. Altman, R. El Azouzi, Y. Hayel: Evolutionary Games in Wireless Networks. IEEE Transactions on Systems, Man, and Cybernetics, Part B 40(3): 634–646 (2010)</span> </li> <li id="cite_note-66"><span class="mw-cite-backlink"><b><a href="#cite_ref-66">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFHammondAxelrod2006" class="citation journal cs1">Hammond, Ross A.; Axelrod, Robert (2006). <a rel="nofollow" class="external text" href="http://egtheory.wordpress.com/2012/06/13/evolution-of-ethnocentrism/">"The Evolution of Ethnocentrism"</a>. <i>Journal of Conflict Resolution</i>. <b>50</b> (6): 926–936. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1177%2F0022002706293470">10.1177/0022002706293470</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:9613947">9613947</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+Conflict+Resolution&rft.atitle=The+Evolution+of+Ethnocentrism&rft.volume=50&rft.issue=6&rft.pages=926-936&rft.date=2006&rft_id=info%3Adoi%2F10.1177%2F0022002706293470&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A9613947%23id-name%3DS2CID&rft.aulast=Hammond&rft.aufirst=Ross+A.&rft.au=Axelrod%2C+Robert&rft_id=http%3A%2F%2Fegtheory.wordpress.com%2F2012%2F06%2F13%2Fevolution-of-ethnocentrism%2F&rfr_id=info%3Asid%2Fen.wikipedia.org%3AEvolutionary+game+theory" class="Z3988"></span></span> </li> <li id="cite_note-67"><span class="mw-cite-backlink"><b><a href="#cite_ref-67">^</a></b></span> <span class="reference-text">Kaznatcheev, A. (2010, March). <a rel="nofollow" class="external text" href="http://www.cs.mcgill.ca/~akazna/kaznatcheev20100910.pdf">Robustness of ethnocentrism to changes in inter-personal interactions</a>. In <i>Complex Adaptive Systems–AAAI Fall Symposium</i>.</span> </li> <li id="cite_note-68"><span class="mw-cite-backlink"><b><a href="#cite_ref-68">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFJee,_J.Sundstrom,_A.Massey,_S.E.Mishra,_B.2013" class="citation journal cs1">Jee, J.; Sundstrom, A.; Massey, S.E.; Mishra, B. (2013). <a rel="nofollow" class="external text" href="https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3785830">"What can information-asymmetric games tell us about the context of Crick's 'Frozen Accident'?"</a>. <i>Journal of the Royal Society Interface</i>. <b>10</b> (88): 20130614. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1098%2Frsif.2013.0614">10.1098/rsif.2013.0614</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/PMC3785830">3785830</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/23985735">23985735</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+the+Royal+Society+Interface&rft.atitle=What+can+information-asymmetric+games+tell+us+about+the+context+of+Crick%27s+%27Frozen+Accident%27%3F&rft.volume=10&rft.issue=88&rft.pages=20130614&rft.date=2013&rft_id=https%3A%2F%2Fwww.ncbi.nlm.nih.gov%2Fpmc%2Farticles%2FPMC3785830%23id-name%3DPMC&rft_id=info%3Apmid%2F23985735&rft_id=info%3Adoi%2F10.1098%2Frsif.2013.0614&rft.au=Jee%2C+J.&rft.au=Sundstrom%2C+A.&rft.au=Massey%2C+S.E.&rft.au=Mishra%2C+B.&rft_id=https%3A%2F%2Fwww.ncbi.nlm.nih.gov%2Fpmc%2Farticles%2FPMC3785830&rfr_id=info%3Asid%2Fen.wikipedia.org%3AEvolutionary+game+theory" class="Z3988"></span></span> </li> </ol></div> <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=Evolutionary_game_theory&action=edit&section=28" title="Edit section: Further reading"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li>Davis, Morton; "Game Theory – A Nontechnical Introduction", Dover Books, <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/0-486-29672-5" title="Special:BookSources/0-486-29672-5">0-486-29672-5</a></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFDawkins2006" class="citation book cs1"><a href="/wiki/Richard_Dawkins" title="Richard Dawkins">Dawkins, Richard</a> (2006). <i><a href="/wiki/The_Selfish_Gene" title="The Selfish Gene">The Selfish Gene</a></i> (30th anniversary ed.). Oxford: Oxford University Press. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-19-929115-1" title="Special:BookSources/978-0-19-929115-1"><bdi>978-0-19-929115-1</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=The+Selfish+Gene&rft.place=Oxford&rft.edition=30th+anniversary&rft.pub=Oxford+University+Press&rft.date=2006&rft.isbn=978-0-19-929115-1&rft.aulast=Dawkins&rft.aufirst=Richard&rfr_id=info%3Asid%2Fen.wikipedia.org%3AEvolutionary+game+theory" class="Z3988"></span></li> <li>Dugatkin and Reeve; "Game Theory and Animal Behavior", Oxford 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/0-19-513790-6" title="Special:BookSources/0-19-513790-6">0-19-513790-6</a></li> <li>Hofbauer and Sigmund; "Evolutionary Games and Population Dynamics", 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/0-521-62570-X" title="Special:BookSources/0-521-62570-X">0-521-62570-X</a></li> <li>Kohn, Marek; "A Reason for Everything", Faber and Faber, <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/0-571-22393-1" title="Special:BookSources/0-571-22393-1">0-571-22393-1</a></li> <li>Li Richter and Lehtonen (Eds.) "Half a century of evolutionary games: a synthesis of theory, application and future directions", Philosophical Transactions of the Royal Society B, <a rel="nofollow" class="external text" href="https://royalsocietypublishing.org/toc/rstb/2023/378/1876">Volume 378, Issue 1876</a></li> <li>Sandholm, William H.; "Population Games and Evolutionary Dynamics", The MIT 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/0262195879" title="Special:BookSources/0262195879">0262195879</a></li> <li>Segerstrale, Ullica; "Nature's Oracle – The life and work of W.D. Hamilton", Oxford University Press, 2013, <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/978-0-19-860727-4" title="Special:BookSources/978-0-19-860727-4">978-0-19-860727-4</a></li> <li><a href="/wiki/Karl_Sigmund" title="Karl Sigmund">Sigmund, Karl</a>; "Games of Life", Penguin Books, also Oxford University Press, 1993, <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/0198547838" title="Special:BookSources/0198547838">0198547838</a></li> <li>Vincent and Brown; "Evolutionary Game Theory, Natural Selection and Darwinian Dynamics", 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/0-521-84170-4" title="Special:BookSources/0-521-84170-4">0-521-84170-4</a></li></ul> <div class="mw-heading mw-heading2"><h2 id="External_links">External links</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Evolutionary_game_theory&action=edit&section=29" title="Edit section: External links"><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 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.plainlist ol,.mw-parser-output .plainlist ul{line-height:inherit;list-style:none;margin:0;padding:0}.mw-parser-output .plainlist ol li,.mw-parser-output .plainlist ul li{margin-bottom:0}</style> <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/Evolutionary_game_theory" class="extiw" title="q:Special:Search/Evolutionary game theory">Evolutionary game theory</a></b></i>.</div></div> </div> <ul><li><a rel="nofollow" class="external text" href="https://royalsocietypublishing.org/toc/rstb/2023/378/1876">Theme issue 'Half a century of evolutionary games: a synthesis of theory, application and future directions' (2023)</a></li> <li><a rel="nofollow" class="external text" href="http://plato.stanford.edu/entries/game-evolutionary/">Evolutionary game theory at the Stanford Encyclopedia of Philosophy</a></li> <li><a rel="nofollow" class="external text" href="https://web.archive.org/web/20070609172509/http://www.ethics.ubc.ca/eame/">Evolving Artificial Moral Ecologies at The Centre for Applied Ethics, University of British Columbia</a></li> <li><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.youtube.com/playlist?list=PLVV0r6CmEsFzJSvAc4MBuUP_GrjO1lLHp">"Life and work of John Maynard Smith, interviewed by Richard Dawkins"</a>. <i><a href="/wiki/Web_of_Stories" title="Web of Stories">Web of Stories</a></i>. 1997 – via YouTube.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=Web+of+Stories&rft.atitle=Life+and+work+of+John+Maynard+Smith%2C+interviewed+by+Richard+Dawkins&rft.date=1997&rft_id=https%3A%2F%2Fwww.youtube.com%2Fplaylist%3Flist%3DPLVV0r6CmEsFzJSvAc4MBuUP_GrjO1lLHp&rfr_id=info%3Asid%2Fen.wikipedia.org%3AEvolutionary+game+theory" class="Z3988"></span> (via <a rel="nofollow" class="external text" href="https://www.webofstories.com/play/john.maynard.smith/1">Web of Stories</a>)</li></ul> <div class="navbox-styles"><style data-mw-deduplicate="TemplateStyles:r1129693374">.mw-parser-output .hlist dl,.mw-parser-output .hlist ol,.mw-parser-output .hlist ul{margin:0;padding:0}.mw-parser-output .hlist dd,.mw-parser-output .hlist dt,.mw-parser-output .hlist li{margin:0;display:inline}.mw-parser-output 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<li><a href="/wiki/Genetic_linkage" title="Genetic linkage">Genetic linkage</a></li> <li><a href="/wiki/Identity_by_descent" title="Identity by descent">Identity by descent</a></li> <li><a href="/wiki/Linkage_disequilibrium" title="Linkage disequilibrium">Linkage disequilibrium</a></li> <li><a href="/wiki/Fisher%27s_fundamental_theorem_of_natural_selection" title="Fisher's fundamental theorem of natural selection">Fisher's fundamental theorem</a></li> <li><a href="/wiki/Neutral_theory_of_molecular_evolution" title="Neutral theory of molecular evolution">Neutral theory</a></li> <li><a href="/wiki/Shifting_balance_theory" title="Shifting balance theory">Shifting balance theory</a></li> <li><a href="/wiki/Price_equation" title="Price equation">Price equation</a></li> <li><a href="/wiki/Coefficient_of_inbreeding" title="Coefficient of inbreeding">Coefficient of inbreeding</a></li> <li><a href="/wiki/Coefficient_of_relationship" title="Coefficient of relationship">Coefficient of relationship</a></li> <li><a href="/wiki/Selection_coefficient" title="Selection coefficient">Selection coefficient</a></li> <li><a href="/wiki/Fitness_(biology)" title="Fitness (biology)">Fitness</a></li> <li><a href="/wiki/Heritability" title="Heritability">Heritability</a></li> <li><a href="/wiki/Population_structure_(genetics)" title="Population structure (genetics)">Population structure</a></li> <li><a href="/wiki/Constructive_neutral_evolution" title="Constructive neutral evolution">Constructive neutral evolution</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="text-align:center;;width:1%"><a href="/wiki/Natural_selection" title="Natural selection">Selection</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/Natural_selection" title="Natural selection">Natural</a></li> <li><a href="/wiki/Selective_breeding" title="Selective breeding">Artificial</a></li> <li><a href="/wiki/Sexual_selection" title="Sexual selection">Sexual</a></li> <li><a href="/wiki/Ecological_selection" class="mw-redirect" title="Ecological selection">Ecological</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="text-align:center;;width:1%"><div style="display: inline-block; line-height: 1.2em; padding: .1em 0; line-height:1.1em;">Effects of selection<br />on genomic variation</div></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/Genetic_hitchhiking" title="Genetic hitchhiking">Genetic hitchhiking</a></li> <li><a href="/wiki/Negative_selection_(natural_selection)" title="Negative selection (natural selection)">Background selection</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="text-align:center;;width:1%"><a href="/wiki/Genetic_drift" title="Genetic drift">Genetic drift</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/Small_population_size" title="Small population size">Small population size</a></li> <li><a href="/wiki/Population_bottleneck" title="Population bottleneck">Population bottleneck</a></li> <li><a href="/wiki/Founder_effect" title="Founder effect">Founder effect</a></li> <li><a href="/wiki/Coalescent_theory" title="Coalescent theory">Coalescence</a></li> <li><a href="/wiki/Balding%E2%80%93Nichols_model" title="Balding–Nichols model">Balding–Nichols model</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="text-align:center;;width:1%">Founders</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/Ronald_Fisher" title="Ronald Fisher">R. A. Fisher</a></li> <li><a href="/wiki/J._B._S._Haldane" title="J. B. S. Haldane">J. B. S. Haldane</a></li> <li><a href="/wiki/Sewall_Wright" title="Sewall Wright">Sewall Wright</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="text-align:center;;width:1%">Related topics</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/Biogeography" title="Biogeography">Biogeography</a></li> <li><a href="/wiki/Evolution" title="Evolution">Evolution</a></li> <li><a class="mw-selflink selflink">Evolutionary game theory</a></li> <li><a href="/wiki/Fitness_landscape" title="Fitness landscape">Fitness landscape</a></li> <li><a href="/wiki/Genetic_genealogy" title="Genetic genealogy">Genetic genealogy</a></li> <li><a href="/wiki/Landscape_genetics" title="Landscape genetics">Landscape genetics</a> and <a href="/wiki/Landscape_genomics" title="Landscape genomics">genomics</a></li> <li><a href="/wiki/Microevolution" title="Microevolution">Microevolution</a></li> <li><a href="/wiki/Population_genomics" title="Population genomics">Population genomics</a></li> <li><a href="/wiki/Phylogeography" title="Phylogeography">Phylogeography</a></li> <li><a href="/wiki/Quantitative_genetics" title="Quantitative genetics">Quantitative genetics</a></li></ul> </div></td></tr><tr><td class="navbox-abovebelow" colspan="2" style="text-align:center;"><div> <ul><li><a href="/wiki/Index_of_evolutionary_biology_articles" title="Index of evolutionary biology articles">Index of evolutionary biology articles</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="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 href="/wiki/Game_theory" title="Game theory">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 class="mw-selflink selflink">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 authority-control" aria-label="Navbox" style="padding:3px"><table class="nowraplinks hlist navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Help:Authority_control" title="Help:Authority control">Authority control databases</a>: National <span class="mw-valign-text-top noprint" typeof="mw:File/Frameless"><a href="https://www.wikidata.org/wiki/Q2298789#identifiers" title="Edit this at Wikidata"><img alt="Edit this at Wikidata" src="//upload.wikimedia.org/wikipedia/en/thumb/8/8a/OOjs_UI_icon_edit-ltr-progressive.svg/10px-OOjs_UI_icon_edit-ltr-progressive.svg.png" decoding="async" width="10" height="10" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/8/8a/OOjs_UI_icon_edit-ltr-progressive.svg/15px-OOjs_UI_icon_edit-ltr-progressive.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/8/8a/OOjs_UI_icon_edit-ltr-progressive.svg/20px-OOjs_UI_icon_edit-ltr-progressive.svg.png 2x" data-file-width="20" data-file-height="20" /></a></span></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"><ul><li><span class="uid"><a rel="nofollow" class="external text" href="https://d-nb.info/gnd/4732282-2">Germany</a></span></li></ul></div></td></tr></tbody></table></div>    </div><noscript><img src="https://login.wikimedia.org/wiki/Special:CentralAutoLogin/start?type=1x1" alt="" width="1" height="1" style="border: none; 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