Evolutionarily Stable Strategies of Random Games, and the Vertices of Random Polygons

Sergiu Hart, Yosef Rinott and Benjamin Weiss ()

Discussion Paper Series from The Federmann Center for the Study of Rationality, the Hebrew University, Jerusalem

Abstract: An evolutionarily stable strategy (ESS) is an equilibrium strategy that is immune to invasions by rare alternative ("mutant") 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 "almost every large" 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 "exponential and faster decreasing tails" (e.g., uniform, normal, exponential); and (ii) it converges to 1 - 1/sqrt(e) for distributions F with "slower than exponential decreasing tails" (e.g., lognormal, Pareto, Cauchy). 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).

Date: 2007-01
New Economics Papers: this item is included in nep-evo and nep-gth
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Citations: View citations in EconPapers (2)

Published in Annals of Applied Probability 18 (2008), 1, 259-287

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http://www.ma.huji.ac.il/hart/abs/ess.html (text/html)

Related works:
Working Paper: Evolutionarily stable strategies of random games, and the vertices of random polygons (2008)
Working Paper: Evolutionarily Stable Strategies of Random Games, and the Vertices of Random Polygons (2007)
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