Document Zbl 1489.91043

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Games Appl.</a> <a href="/?q=in%3A480750" title="Articles in this Issue">12, No. 1, 214-236 (2022)</a>. </div> <div class="abstract">Summary: Individual behaviors play an essential role in the dynamics of transmission of infectious diseases, including COVID-19. This paper studies a dynamic game model that describes the social distancing behaviors during an epidemic, assuming a continuum of players and individual infection dynamics. The evolution of the players’ infection states follows a variant of the well-known SIR dynamics. We assume that the players are not sure about their infection state, and thus, they choose their actions based on their individually perceived probabilities of being susceptible, infected, or removed. The cost of each player depends both on her infection state and on the contact with others. We prove the existence of a Nash equilibrium and characterize Nash equilibria using nonlinear complementarity problems. We then exploit some monotonicity properties of the optimal policies to obtain a reduced-order characterization for Nash equilibrium and reduce its computation to the solution of a low-dimensional optimization problem. It turns out that, even in the symmetric case, where all the players have the same parameters, players may have very different behaviors. We finally present some numerical studies that illustrate this interesting phenomenon and investigate the effects of several parameters, including the players’ vulnerability, the time horizon, and the maximum allowed actions, on the optimal policies and the players’ costs.</div> <div class="clear"></div> <br> <div class="citations"><div class="clear"><a href="/?q=rf%3A7512082">Cited in <strong>4</strong> Documents</a></div></div> <div class="classification"> <h3>MSC:</h3> <table><tr> <td> <a class="mono" href="/classification/?q=cc%3A91A25" title="MSC2020">91A25</a> </td> <td class="space"> Dynamic games </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A92D30" title="MSC2020">92D30</a> </td> <td class="space"> Epidemiology </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A91A80" title="MSC2020">91A80</a> </td> <td class="space"> Applications of game theory </td> </tr></table> </div><div class="keywords"> <h3>Keywords:</h3><a href="/?q=ut%3ACOVID-19+pandemic">COVID-19 pandemic</a>; <a href="/?q=ut%3Agames+of+social+distancing">games of social distancing</a>; <a href="/?q=ut%3Aepidemics+modeling+and+control">epidemics modeling and control</a>; <a href="/?q=ut%3ANash+games">Nash games</a>; <a href="/?q=ut%3Anonlinear+complementarity+problems">nonlinear complementarity problems</a></div>  <div class="modal fade" id="metadataModal" tabindex="-1" role="dialog" aria-labelledby="myModalLabel"> <div class="modal-dialog" role="document"> <div class="modal-content"> <div class="modal-header"> <button type="button" class="close" data-dismiss="modal" aria-label="Close"><span aria-hidden="true">×</span></button> <h4 class="modal-title" id="myModalLabel">Cite</h4> </div> <div class="modal-body"> <div class="form-group"> <label for="select-output" class="control-label">Format</label> <select id="select-output" class="form-control" aria-label="Select Metadata format"></select> </div> <div class="form-group"> <label for="metadataText" class="control-label">Result</label> <textarea class="form-control" id="metadataText" rows="10" style="min-width: 100%;max-width: 100%"></textarea> </div> <div id="metadata-alert" class="alert alert-danger" role="alert" style="display: none;">  </div> </div> <div class="modal-footer"> <button type="button" class="btn btn-primary" onclick="copyMetadata()">Copy to clipboard</button> <button type="button" class="btn btn-default" data-dismiss="modal">Close</button> </div> </div> </div> </div> <div class="functions clearfix"> <div class="function">  <a type="button" class="btn btn-default btn-xs pdf" data-toggle="modal" data-target="#metadataModal" data-itemtype="Zbl" data-itemname="Zbl 1489.91043" data-ciurl="/ci/07512082" data-biburl="/bibtex/07512082.bib" data-amsurl="/amsrefs/07512082.bib" data-xmlurl="/xml/07512082.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/07512082.pdf" title="Zbl 1489.91043 as PDF">Review PDF</a> </div> <div class="fulltexts"> <span class="fulltext">Full Text:</span> <a class="btn btn-default btn-xs" type="button" href="https://doi.org/10.1007/s13235-021-00403-1" aria-label="DOI for “Dynamic games of social distancing during an epidemic: analysis of asymmetric solutions”" title="10.1007/s13235-021-00403-1">DOI</a> <a class="btn btn-default btn-xs" type="button" href="https://arxiv.org/abs/2105.12431"title="Note: arXiv document may differ from published version">arXiv</a> </div> <div class="sfx" style="float: right;"> </div> </div> <div class="references"> <h3>References:</h3> <table><tr> <td>[1]</td> <td class="space">Allen LJ, Brauer F, Van den Driessche P, Wu J (2008) Mathematical epidemiology, vol 1945, Springer · <a href="/1159.92034" class="nowrap">Zbl 1159.92034</a></td> </tr><tr> <td>[2]</td> <td class="space">Amaral MA, de Oliveira MM, Javarone MA (2020) An epidemiological model with voluntary quarantine strategies governed by evolutionary game dynamics. arXiv preprint arXiv:2008.05979</td> </tr><tr> <td>[3]</td> <td class="space">Amini H, Minca A (2020) Epidemic spreading and equilibrium social distancing in heterogeneous networks</td> </tr><tr> <td>[4]</td> <td class="space">Aurell A, Carmona R, Dayanikli G, Lauriere M (2020) Optimal incentives to mitigate epidemics: a Stackelberg mean field game approach. arXiv preprint arXiv:2011.03105</td> </tr><tr> <td>[5]</td> <td class="space">Bertsekas DP (1997) Nonlinear programming. 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