Regret Matching with Finite Memory
 Rene Saran,
 Roberto Serrano
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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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 Title
 Regret Matching with Finite Memory
 Open Access
 Available under Open Access This content is freely available online to anyone, anywhere at any time.
 Journal

Dynamic Games and Applications
Volume 2, Issue 1 , pp 160175
 Cover Date
 20120301
 DOI
 10.1007/s1323501100218
 Print ISSN
 21530785
 Online ISSN
 21530793
 Publisher
 SP Birkhäuser Verlag Boston
 Additional Links
 Topics
 Keywords

 Regret matching
 Nash equilibria
 Closed sets under same or better replies
 Correlated equilibria
 Authors

 Rene Saran ^{(1)}
 Roberto Serrano ^{(2)} ^{(3)}
 Author Affiliations

 1. Maastricht University, Maastricht, The Netherlands
 2. Brown University, Providence, USA
 3. IMDEA Social Sciences Institute, Madrid, Spain