Limiting distributions of the number of pure strategy Nash equilibria in n-person games
- 105 Downloads
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 consider both the cases where all players have strictly and weakly ordinal preferences over their outcomes. For both cases, we 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. We also find, for each case, the distribution of the number of pure strategy Nash equilibria when the number of strategies of one player goes to infinity, while those of the other players remain finite.
KeywordsNash Equilibrium Economic Theory Game Theory Poisson Distribution Pure Strategy
Unable to display preview. Download preview PDF.
- Chen LHY (1975) Poisson Approximation for Dependent Trials. Ann. Prob. 3: 534–545Google Scholar
- Chung KL (1974) A Course in Probability Theory, Second Edition. New York: Academic Press, p. 92Google Scholar
- Dresher M (1970) Probability of A Pure Equilibrium Point in n-Person Games. J of Combinatorial Theory 8: 134–145Google Scholar
- Gelbaum BR, Olmsted JMH (1964) Counterexamples in Analysis. San Francisco: Holden-Day Inc., p. 117Google Scholar
- Goldberg K, Goldman AJ, and Newman M (1968) The Probability of an Equilibrium Point. J of Research of National Bureau of Standards U.S.A., 72 B: 93–101Google Scholar
- Nash JF jr (1951) Noncooperative Games. Ann. Math. 54: 286–295Google Scholar
- Powers IY (1986) The Distribution of the Number of Pure Strategy Nash Equilibria in n-Person Games, Part 1 of Three Essays in Game Theory, Ph. D. Dissertation, Yale UniversityGoogle Scholar