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Regret matching with finite memory

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  • Rene Saran

    ()
    (Maastricht University)

  • Roberto Serrano

    ()
    (Brown University)

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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Bibliographic Info

Paper provided by Instituto Madrileño de Estudios Avanzados (IMDEA) Ciencias Sociales in its series Working Papers with number 2010-10.

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Date of creation: 04 Jun 2010
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Publication status: Published in Dynamic Games and Applications 2(1), March 2012: 160-175
Handle: RePEc:imd:wpaper:wp2010-10

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Keywords: regret matching; nash equilibria; closed sets under same or better replies; correlated equilibria;

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References

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  1. Andriy Zapechelnyuk, 2008. "Better-Reply Dynamics with Bounded Recall," Discussion Papers 2, Kyiv School of Economics, revised Mar 2008.
  2. Sergiu Hart, 2004. "Adaptive Heuristics," Levine's Bibliography 122247000000000471, UCLA Department of Economics.
  3. Saran Rene & Serrano Roberto, 2010. "Ex-Post Regret Learning in Games with Fixed and Random Matching: The Case of Private Values," Research Memorandum 032, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
  4. Fudenberg, Drew & Levine, David K., 1995. "Consistency and cautious fictitious play," Journal of Economic Dynamics and Control, Elsevier, vol. 19(5-7), pages 1065-1089.
  5. Ritzberger, Klaus & Weibull, Jörgen W., 1993. "Evolutionary Selection in Normal Form Games," Working Paper Series 383, Research Institute of Industrial Economics.
  6. Josephson, Jens & Matros, Alexander, 2004. "Stochastic imitation in finite games," Games and Economic Behavior, Elsevier, vol. 49(2), pages 244-259, November.
  7. Young, H Peyton, 1993. "The Evolution of Conventions," Econometrica, Econometric Society, vol. 61(1), pages 57-84, January.
  8. Sergiu Hart & Andreu Mas-Colell, 1996. "A simple adaptive procedure leading to correlated equilibrium," Economics Working Papers 200, Department of Economics and Business, Universitat Pompeu Fabra, revised Dec 1996.
  9. 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, Brown University, Department of Economics.
  10. Hurkens Sjaak, 1995. "Learning by Forgetful Players," Games and Economic Behavior, Elsevier, vol. 11(2), pages 304-329, November.
  11. Lehrer, Ehud & Solan, Eilon, 2009. "Approachability with bounded memory," Games and Economic Behavior, Elsevier, vol. 66(2), pages 995-1004, July.
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Cited by:
  1. 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, Brown University, Department of Economics.
  2. Saran Rene & Serrano Roberto, 2010. "Ex-Post Regret Learning in Games with Fixed and Random Matching: The Case of Private Values," Research Memorandum 032, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).

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