Please use this identifier to cite or link to this item: https://hdl.handle.net/10419/233287 
Year of Publication: 
2011
Series/Report no.: 
Discussion paper No. 71
Publisher: 
Aboa Centre for Economics (ACE), Turku
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.
Subjects: 
random games
pure Nash equilibria
n players
JEL: 
C62
C72
Document Type: 
Working Paper

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