Three Problems in Learning Mixed-Strategy Nash Equilibria

Abstract

This paper discusses three problems that can prevent the convergence of learning mechanisms to mixed-strategy Nash equilibria. First, while players′ expectations may converge to a mixed equilibrium, the strategies played typically fail to converge. Second, even in 2 × 2 games, fictitious play can produce a sequence of frequency distributions in which the marginal frequencies converge to equilibrium mixed strategies but the joint frequencies violate independence. Third, in a three-player matching-pennies game with a unique equilibrium, it is shown that if players learn as Bayesian statisticians then the equilibrium is locally unstable. Journal of Economic Literature Classification Numbers: C72, C73, D83.