Regret matching with finite memory

Rene Saran () and Roberto Serrano
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Rene Saran: Maastricht University

No 2010-10, Working Papers from Instituto Madrileño de Estudios Avanzados (IMDEA) Ciencias Sociales

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.

Keywords: regret matching; nash equilibria; closed sets under same or better replies; correlated equilibria (search for similar items in EconPapers)
JEL-codes: C72 C73 D83 (search for similar items in EconPapers)
Date: 2010-06-04
New Economics Papers: this item is included in nep-gth
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Citations: View citations in EconPapers (2)

Published in Dynamic Games and Applications 2(1), March 2012: 160-175

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Related works:
Journal Article: Regret Matching with Finite Memory (2012)
Working Paper: Regret Matching with Finite Memory (2010)
Working Paper: Regret Matching with Finite Memory (2010)
Working Paper: Regret matching with finite memory (2010)
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