On the Convergence of Fictitious Play

Vijay Krishna · Tomas Sjöström

78 citations0/0 files storedMathematics of Operations Research

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Game Theory and Applications Game Theory and Voting Systems Evolutionary Game Theory and Cooperation

Abstract

We study the Brown-Robinson fictitious play process for non-zero sum games. We show that, in general, fictitious play cannot converge cyclically to a mixed strategy equilibrium in which both players use more than two pure strategies.

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1973Games with randomly disturbed payoffs: A new rationale for mixed-strategy equilibrium points 1951An Iterative Method of Solving a Game 1991Comments on the Interpretation of Game Theory 1993Learning Mixed Equilibria 1991Stability and Perfection of Nash Equilibria 1993Three Problems in Learning Mixed-Strategy Nash Equilibria 1973Oddness of the number of equilibrium points: A new proof

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2008Learning in games with unstable equilibria 2018On Best-Response Dynamics in Potential Games 1997Learning from Personal Experience: One Rational Guy and the Justification of Myopia 2004Unified Convergence Proofs of Continuous-Time Fictitious Play 1998On the Nonconvergence of Fictitious Play in Coordination Games 2022The Confluence of Networks, Games, and Learning a Game-Theoretic Framework for Multiagent Decision Making Over Networks 2000Learning Purified Mixed Equilibria

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