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Regret Matching with Finite Memory

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  • Rene Saran
  • Roberto Serrano

Abstract

We consider the regret matching process with finite memory. For general games in normal form, it is shown that any recurrent class of the dynamics must be such that the action profiles that appear in it constitute a closed set under the “same or better reply†correspondence (CUSOBR set) that does not contain a smaller product set that is closed under “same or better replies,†i.e., a smaller PCUSOBR set. Two characterizations of the recurrent classes are offered. First, for the class of weakly acyclic games under better replies, each recurrent class is monomorphic and corresponds to each pure Nash equilibrium.Second, for a modified process with random sampling, if the sample size is sufficiently small with respect to the memory bound, the recurrent classes consist of action profiles that are minimal PCUSOBR sets. Our results are used in a robust example that shows that the limiting empirical distribution of play can be arbitrarily far from correlated equilibria for any large but finite choice of the memory bound.
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Suggested Citation

  • Rene Saran & Roberto Serrano, 2012. "Regret Matching with Finite Memory," Dynamic Games and Applications, Springer, vol. 2(1), pages 160-175, March.
    • Handle: RePEc:spr:dyngam:v:2:y:2012:i:1:p:160-175
    DOI: 10.1007/s13235-011-0021-8
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    Cited by:

    1. Damjanovic, Vladislav, 2017. "Two “little treasure games” driven by unconditional regret," Economics Letters, Elsevier, vol. 150(C), pages 99-103.
    2. Rene Saran & Roberto Serrano, 2010. "Ex-post regret learning in games with fixed and random matching: The case of private values," Working Papers 2010-11, Instituto Madrileño de Estudios Avanzados (IMDEA) Ciencias Sociales.
    3. Saran, Rene & Serrano, Roberto, 2014. "Ex-post regret heuristics under private values (I): Fixed and random matching," Journal of Mathematical Economics, Elsevier, vol. 54(C), pages 97-111.

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    More about this item

    Keywords

    Regret matching; Nash equilibria; Closed sets under same or better replies; Correlated equilibria;
    All these keywords.

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games
    • D83 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Search; Learning; Information and Knowledge; Communication; Belief; Unawareness

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