In this paper, we study the number of pure strategy Nash equilibria in a “random” n-person non-cooperative game in which all players have a countable number of strategies. We provide explicit expressions for the expected number of pure strategy Nash Equilibria, and show that the distribution of the number of pure strategy Nash Equilibria approaches the Poisson distribution with mean 1 as the numbers of strategies of two or more players go to inﬁnity.
Pure strategy, Nash equilibria, Random n-person game, Strictly and weakly ordinal game
JEL Classification Codes: 026
Published in International Journal of Game Theory (March 1990), 19(3): 277-286 [DOI]