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Epsilon-equilibria of perturbed games

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

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.

Suggested Citation

  • Jackson, Matthew O. & Rodriguez-Barraquer, Tomas & Tan, Xu, 2012. "Epsilon-equilibria of perturbed games," Games and Economic Behavior, Elsevier, vol. 75(1), pages 198-216.
  • Handle: RePEc:eee:gamebe:v:75:y:2012:i:1:p:198-216
    DOI: 10.1016/j.geb.2011.09.007
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    References listed on IDEAS

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    Cited by:

    1. Barbie, Martin & Gupta, Abhishek, 2014. "The topology of information on the space of probability measures over Polish spaces," Journal of Mathematical Economics, Elsevier, vol. 52(C), pages 98-111.
    2. Zhijun Chen & Chongwoo Choe & Noriaki Matsushima, 2018. "Competitive Personalized Pricing," ISER Discussion Paper 1023, Institute of Social and Economic Research, Osaka University.
    3. Chen, Yi-Chun & Takahashi, Satoru & Xiong, Siyang, 2014. "The robust selection of rationalizability," Journal of Economic Theory, Elsevier, vol. 151(C), pages 448-475.
    4. Lu, Shih En, 2017. "Coordination-free equilibria in cheap talk games," Journal of Economic Theory, Elsevier, vol. 168(C), pages 177-208.

    More about this item

    Keywords

    Epsilon-equilibrium; Epsilon-Nash equilibrium; Electronic mail game; Global games; Bayesian games; Trembling-hand perfection; Nash equilibrium; Lower hemi-continuity;

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design

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