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Epsilon-equilibria of perturbed games

  • Jackson, Matthew O.
  • Rodriguez-Barraquer, Tomas
  • Tan, Xu

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.

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Article provided by Elsevier in its journal Games and Economic Behavior.

Volume (Year): 75 (2012)
Issue (Month): 1 ()
Pages: 198-216

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Handle: RePEc:eee:gamebe:v:75:y:2012:i:1:p:198-216
Contact details of provider: Web page: http://www.elsevier.com/locate/inca/622836

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