Epsilon-Equilibria of Perturbed Games
Matthew O. Jackson
Stanford University - Department of Economics; Santa Fe Institute; Canadian Institute for Advanced Research (CIFAR)
Tomás Rodríguez Barraquer
Hebrew University of Jerusalem - Center for the Study of Rationality
Stanford University - Department of Economics
August 26, 2010
Games and Economic Behavior, Volume 75, Issue 1, May 2012, Pages 198–216
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.
Number of Pages in PDF File: 36
Keywords: epsilon-equilibrium, epsilon-Nash equilibrium, electronic mail game, global games, Bayesian games, trembling hand perfection, Nash equilibrium, lower hemi-continuity
JEL Classification: C72, D82Accepted Paper Series
Date posted: August 13, 2010 ; Last revised: January 3, 2013
© 2013 Social Science Electronic Publishing, Inc. All Rights Reserved.
This page was processed by apollo2 in 0.437 seconds