Epsilon-equilibria of perturbed games

Matthew Jackson, Tomás Rodríguez and Xu Tan

Games and Economic Behavior, 2012, vol. 75, issue 1, 198-216

Abstract: 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 ε-equilibria converging to the given equilibrium of the original game. We strengthen the conclusion to show that the approaching equilibria are interim ε-equilibria (ε-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 Seltenʼs (1975) definition of trembling-hand perfect equilibrium, Rubinsteinʼs (1989) analysis of the electronic mail game, and Carlsson and van Dammeʼs (1993) global games analysis, among others.

Keywords: Epsilon-equilibrium; Epsilon-Nash equilibrium; Electronic mail game; Global games; Bayesian games; Trembling-hand perfection; Nash equilibrium; Lower hemi-continuity (search for similar items in EconPapers)
JEL-codes: C72 D82 (search for similar items in EconPapers)
Date: 2012
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (11)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:gamebe:v:75:y:2012:i:1:p:198-216

DOI: 10.1016/j.geb.2011.09.007

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