Regret Matching with Finite Memory

Brown University Economic Working Paper

16 Pages Posted: 4 Jun 2010

See all articles by Rene Saran

Rene Saran

University of Cincinnati - Department of Economics

Roberto Serrano

Brown University

Date Written: June 4, 2010


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 Reply

JEL Classification: C72, C73, D83

Suggested Citation

Saran, Rene and Serrano, Roberto, Regret Matching with Finite Memory (June 4, 2010). Brown University Economic Working Paper, Available at SSRN: or

Rene Saran (Contact Author)

University of Cincinnati - Department of Economics ( email )

Carl H. Lindner Hall 2925 Campus Green Drive
PO Box 0371
Cincinnati, OH 45221-0211
United States

Roberto Serrano

Brown University ( email )

64 Waterman Street
Providence, RI 02912
United States
401-863-1036 (Phone)
401-863-1970 (Fax)

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