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A Simple Adaptive Procedure Leading to Correlated Equilibrium

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  • Sergiu Hart

    (The Hebrew University of Jerusalem)

  • Andreu Mas-Colell

    (Universitat Pompeu Fabra, Barcelona)

Abstract

We propose a new and simple adaptive procedure for playing a game: "regret-matching." In this procedure, players depart from their current play with probabilities that are proportional to measures of regret for not having used other strategies in the past. It is shown that our adaptive procedure guarantees that, with probability one, the empirical distributions of play converge to the set of correlated equilibria of the game. To compute these regret measures, a player needs to know his payoff function and the history of play. We also offer a variation where every player knows only his own realized payoff history (but not his payoff function).

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File URL: http://128.118.178.162/eps/game/papers/9703/9703006.ps.gz
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Bibliographic Info

Paper provided by EconWPA in its series Game Theory and Information with number 9703006.

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Date of creation: 24 Mar 1997
Date of revision: 24 Mar 1997
Handle: RePEc:wpa:wuwpga:9703006

Note: January 1997. Revised: October 1997. Paper + 3 figures (postscript). Also available at URL below
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Web page: http://128.118.178.162

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  1. Mertens, J.-F., 1986. "Repeated games," CORE Discussion Papers 1986024, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  2. Drew Fudenberg & David K. Levine, 1997. "Conditional Universal Consistency," Levine's Working Paper Archive 471, David K. Levine.
  3. Drew Fudenberg & David K. Levine, 1998. "Learning in Games," Levine's Working Paper Archive 2222, David K. Levine.
  4. Robert J. Aumann, 2010. "Correlated Equilibrium as an expression of Bayesian Rationality," Levine's Working Paper Archive 661465000000000377, David K. Levine.
  5. 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.
  6. Nau, Robert F. & McCardle, Kevin F., 1990. "Coherent behavior in noncooperative games," Journal of Economic Theory, Elsevier, vol. 50(2), pages 424-444, April.
  7. C. Sanchirico, 2010. "A Probabilistic Model of Learning in Games," Levine's Working Paper Archive 484, David K. Levine.
  8. Erev, Ido & Roth, Alvin E, 1998. "Predicting How People Play Games: Reinforcement Learning in Experimental Games with Unique, Mixed Strategy Equilibria," American Economic Review, American Economic Association, vol. 88(4), pages 848-81, September.
  9. Aumann, Robert J., 1974. "Subjectivity and correlation in randomized strategies," Journal of Mathematical Economics, Elsevier, vol. 1(1), pages 67-96, March.
  10. Nimrod Megiddo, 1979. "On Repeated Games with Incomplete Information Played by Non-Bayesian Players," Discussion Papers 373, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  11. Foster, Dean P. & Vohra, Rakesh, 1999. "Regret in the On-Line Decision Problem," Games and Economic Behavior, Elsevier, vol. 29(1-2), pages 7-35, October.
  12. Roger B. Myerson, 1995. "Dual Reduction and Elementary Games," Discussion Papers 1133, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  13. Sergiu Hart & Andreu Mas-Colell, 1999. "A general class of adaptative strategies," Economics Working Papers 373, Department of Economics and Business, Universitat Pompeu Fabra.
  14. Colin Camerer & Teck-Hua Ho, 1999. "Experience-weighted Attraction Learning in Normal Form Games," Econometrica, Econometric Society, vol. 67(4), pages 827-874, July.
  15. repec:fth:coluec:9596-22 is not listed on IDEAS
  16. Roth, Alvin E. & Erev, Ido, 1995. "Learning in extensive-form games: Experimental data and simple dynamic models in the intermediate term," Games and Economic Behavior, Elsevier, vol. 8(1), pages 164-212.
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