Distribution of pure Nash equilibria in n-person games with random best replies

Klaus Kultti (), Hannu Salonen and Hannu Vartiainen ()

No 71, Discussion Papers from Aboa Centre for Economics

Abstract: In this paper we study the number of pure strategy Nash equilibria in large finite n-player games. A distinguishing feature of our study is that we allow general - potentially multivalued - best reply correspondences. Given the number K of pure strategies to each player, we assign to each player a distribution over the number of his pure best replies against each strategy profile of his opponents. If the means of these distributions have a limit (mu)i for each player i as the number K of pure strategies goes to infinity, then the limit number of pure equilibria is Poisson distributed with a mean equal to the product of the limit means (mu)i. In the special case when all best reply mappings are equally likely, the probability of at least one pure Nash equilibrium approaches one and the expected number of pure Nash equilibria goes to infinity.

Keywords: random games; pure Nash equilibria; n players (search for similar items in EconPapers)
JEL-codes: C62 C72 (search for similar items in EconPapers)
Pages: 21
Date: 2011-12
New Economics Papers: this item is included in nep-gth, nep-hpe and nep-mic
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (3)

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