{"id":183132,"date":"2007-02-06T00:00:00","date_gmt":"2009-10-31T10:20:38","guid":{"rendered":"https:\/\/www.microsoft.com\/en-us\/research\/msr-research-item\/evolutionarily-stable-strategies-of-random-games-and-the-vertices-of-random-polygons\/"},"modified":"2016-09-09T09:48:52","modified_gmt":"2016-09-09T16:48:52","slug":"evolutionarily-stable-strategies-of-random-games-and-the-vertices-of-random-polygons","status":"publish","type":"msr-video","link":"https:\/\/www.microsoft.com\/en-us\/research\/video\/evolutionarily-stable-strategies-of-random-games-and-the-vertices-of-random-polygons\/","title":{"rendered":"Evolutionarily Stable Strategies of Random Games, and the Vertices of Random Polygons"},"content":{"rendered":"<div class=\"asset-content\">\n<p>An evolutionarily stable strategy (ESS) is an equilibrium strategy that is immune to invasions by rare alternative (&#8220;mutant&#8221;) strategies. Unlike Nash equilibria, ESS do not always exist in finite games. In this paper, we address the question of what happens when the size of the game increases: does an ESS exist for &#8220;almost every large&#8221; game? Letting the entries in the n x n game matrix be randomly chosen according to an underlying distribution F, we study the number of ESS with support of size 2. In particular, we show that, as n goes to infinity, the probability of having such an ESS: (i) converges to 1 for distributions F with &#8220;exponential and faster decreasing tails&#8221; (e.g., uniform, normal, exponential); and (ii) it converges to 1 &#8211; 1\/sqrt(e) for distributions F with &#8220;slower than exponential decreasing tails&#8221; (e.g., lognormal, Pareto, Cauchy).<\/p>\n<p>Our results also imply that the expected number of vertices of the convex hull of n random points in the plane converges to infinity for the distributions in (i), and to 4 for the distributions in (ii).<\/p>\n<p>The talk is based on joint work with Yosef Rinott and Benjamin Weiss.<\/p>\n<\/div>\n<p><!-- .asset-content --><\/p>\n","protected":false},"excerpt":{"rendered":"<p>An evolutionarily stable strategy (ESS) is an equilibrium strategy that is immune to invasions by rare alternative (&#8220;mutant&#8221;) strategies. Unlike Nash equilibria, ESS do not always exist in finite games. In this paper, we address the question of what happens when the size of the game increases: does an ESS exist for &#8220;almost every large&#8221; [&hellip;]<\/p>\n","protected":false},"featured_media":194913,"template":"","meta":{"msr-url-field":"","msr-podcast-episode":"","msrModifiedDate":"","msrModifiedDateEnabled":false,"ep_exclude_from_search":false,"_classifai_error":"","msr_hide_image_in_river":0,"footnotes":""},"research-area":[],"msr-video-type":[],"msr-locale":[268875],"msr-post-option":[],"msr-session-type":[],"msr-impact-theme":[],"msr-pillar":[],"msr-episode":[],"msr-research-theme":[],"class_list":["post-183132","msr-video","type-msr-video","status-publish","has-post-thumbnail","hentry","msr-locale-en_us"],"msr_download_urls":"","msr_external_url":"https:\/\/youtu.be\/GdHuiR1bu_M","msr_secondary_video_url":"","msr_video_file":"","_links":{"self":[{"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-video\/183132","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-video"}],"about":[{"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/types\/msr-video"}],"version-history":[{"count":0,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-video\/183132\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/media\/194913"}],"wp:attachment":[{"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/media?parent=183132"}],"wp:term":[{"taxonomy":"msr-research-area","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/research-area?post=183132"},{"taxonomy":"msr-video-type","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-video-type?post=183132"},{"taxonomy":"msr-locale","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-locale?post=183132"},{"taxonomy":"msr-post-option","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-post-option?post=183132"},{"taxonomy":"msr-session-type","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-session-type?post=183132"},{"taxonomy":"msr-impact-theme","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-impact-theme?post=183132"},{"taxonomy":"msr-pillar","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-pillar?post=183132"},{"taxonomy":"msr-episode","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-episode?post=183132"},{"taxonomy":"msr-research-theme","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-research-theme?post=183132"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}