Evolutionarily Stable Strategies of Random Games and the Facets of Random Polytopes

Ohad Navon

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? We let the entries of an n × n game matrix be independently randomly chosen according to a symmetrical subexponential distribution F, and study the expected number of ESS with support of size d as n ? ?. In a previous paper by Hart, Rinott and Weiss [6] it was shown that this limit is 1 2 for d = 2. This paper deals with the case of d ? 4, and proves the conjecture in [6] (Section 6,c), that the expected number of ESS with support of size d ? 4 is 0. Furthermore, it discusses the classic problem of the number of facets of a convex hull of n random points in Rd, and relates it to the above ESS problem. Given a collection of i.i.d. random points, our result implies that the expected number of facets of their convex hull converges to 2d as n ? ?.

Pages: 44 pages
Date: 2016-09
New Economics Papers: this item is included in nep-gth and nep-hpe
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1) Track citations by RSS feed

Downloads: (external link)
http://ratio.huji.ac.il/sites/default/files/publications/dp702.pdf (application/pdf)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:huj:dispap:dp702

Access Statistics for this paper

More papers in Discussion Paper Series from The Federmann Center for the Study of Rationality, the Hebrew University, Jerusalem Contact information at EDIRC.
Bibliographic data for series maintained by Michael Simkin ().