Epsilon-equilibria of perturbed games
Title: Epsilon-equilibria of perturbed games
Citation: Games and Economic Behavior, 2012, Vol. 75, No. 1, pp. 198-216
ISSN: 1090-2473; 0899-8256
We prove that for any equilibrium of a (Bayesian) game, and any sequence of perturbations of that game, there exists a corresponding sequence of ex-ante e-equilibria converging to the given equilibrium of the original game. We strengthen the conclusion to show that the approaching equilibria are interim e-equilibria (e-best responses for almost all types) if beliefs in the perturbed games converge in a strong-enough sense to the limit beliefs. Therefore, equilibrium selection arguments that are based on perturbations to a game are not robust to slight perturbations in best reply behavior (or to underlying preferences). This applies to many standard equilibrium selections, including Selten's (1975) definition of trembling-hand perfect equilibrium, Rubinstein's (1989) analysis of the electronic mail game, and Carlsson and van Damme's (1993) global games analysis, among others
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