Epsilon-Equilibria of Perturbed Games

36 Pages Posted: 13 Aug 2010 Last revised: 3 Jan 2013

See all articles by Matthew O. Jackson

Matthew O. Jackson

Stanford University - Department of Economics; Santa Fe Institute

Tomás Rodríguez Barraquer

Universidad de los Andes

Xu Tan

University of Washington - Economics

Date Written: August 26, 2010


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 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.

Keywords: epsilon-equilibrium, epsilon-Nash equilibrium, electronic mail game, global games, Bayesian games, trembling hand perfection, Nash equilibrium, lower hemi-continuity

JEL Classification: C72, D82

Suggested Citation

Jackson, Matthew O. and Rodríguez Barraquer, Tomás and Tan, Xu, Epsilon-Equilibria of Perturbed Games (August 26, 2010). Games and Economic Behavior, Volume 75, Issue 1, May 2012, Pages 198–216, Available at SSRN: https://ssrn.com/abstract=1657131

Matthew O. Jackson (Contact Author)

Stanford University - Department of Economics ( email )

Landau Economics Building
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Stanford, CA 94305-6072
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HOME PAGE: http://www.stanford.edu/~jacksonm

Santa Fe Institute

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Santa Fe, NM 87501
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Tomás Rodríguez Barraquer

Universidad de los Andes ( email )

Carrera 1a No. 18A-10
Santafe de Bogota, AA4976

Xu Tan

University of Washington - Economics ( email )

Seattle, WA
United States

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