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; Canadian Institute for Advanced Research (CIFAR)

Tomás Rodríguez Barraquer

Autonomous University of Barcelona

Xu Tan

University of Washington - Economics

Date Written: August 26, 2010

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 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
579 Serra Mall
Stanford, CA 94305-6072
United States
1-650-723-3544 (Phone)

HOME PAGE: http://www.stanford.edu/~jacksonm

Santa Fe Institute

1399 Hyde Park Road
Santa Fe, NM 87501
United States

Canadian Institute for Advanced Research (CIFAR) ( email )

180 Dundas Street West, Suite 1400
Toronto, Ontario
Canada

Tomás Rodríguez Barraquer

Autonomous University of Barcelona ( email )

Plaça Cívica
Cerdañola del Valles
Cerdanyola del Vallès, BARCELONA 08193
Spain

Xu Tan

University of Washington - Economics ( email )

Seattle, WA
United States

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