COWLES FOUNDATION FOR RESEARCH IN ECONOMICS
AT YALE UNIVERSITY

Post Office Box 208281
New Haven, CT 06520-8281

COWLES FOUNDATION DISCUSSION PAPER NO. 799

"Limiting Distributions of the Number of Pure Strategy Nash Equilibria
in n-Person Games"

Imelda Young Powers

August 1986

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.

JEL Classification: 026

Keywords: Pure strategy, Nash equilibria, random n-person game, strictly and weakly ordinal game