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A Simple Adaptive Procedure Leading to Correlated Equilibrium

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  • S. Hart
  • A. Mas-Collel

Abstract

We propose a simple adaptive procedure for playing a game. In this procedure, players depart from their current play with probabilities that are proportional to measures of regret for not having used other strategies (these measures are updated every period). It is shown that our adaptive procedure guaranties that with probability one, the sample 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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Paper provided by David K. Levine in its series Levine's Working Paper Archive with number 572.

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Date of creation: 09 Dec 2010
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Handle: RePEc:cla:levarc:572

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  1. Aumann, Robert J, 1987. "Correlated Equilibrium as an Expression of Bayesian Rationality," Econometrica, Econometric Society, vol. 55(1), pages 1-18, January.
  2. 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.
  3. Sanchirico, Chris William, 1996. "A Probabilistic Model of Learning in Games," Econometrica, Econometric Society, vol. 64(6), pages 1375-93, November.
  4. Fudenberg, Drew & Levine, David, 1995. "Consistency and Cautious Fictitious Play," Scholarly Articles 3198694, Harvard University Department of Economics.
  5. Myerson, Roger B., 1997. "Dual Reduction and Elementary Games," Games and Economic Behavior, Elsevier, vol. 21(1-2), pages 183-202, October.
  6. Drew Fudenberg & David K. Levine, 1998. "Learning in Games," Levine's Working Paper Archive 2222, David K. Levine.
  7. repec:fth:coluec:9596-22 is not listed on IDEAS
  8. Aumann, Robert J., 1974. "Subjectivity and correlation in randomized strategies," Journal of Mathematical Economics, Elsevier, vol. 1(1), pages 67-96, March.
  9. 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.
  10. Colin Camerer & Teck-Hua Ho, 1999. "Experience-weighted Attraction Learning in Normal Form Games," Econometrica, Econometric Society, vol. 67(4), pages 827-874, July.
  11. Drew Fudenberg & David K. Levine, 1997. "Conditional Universal Consistency," Levine's Working Paper Archive 471, David K. Levine.
  12. Mertens, J.-F., 1986. "Repeated games," CORE Discussion Papers 1986024, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  13. Nau, Robert F. & McCardle, Kevin F., 1990. "Coherent behavior in noncooperative games," Journal of Economic Theory, Elsevier, vol. 50(2), pages 424-444, April.
  14. 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.
  15. Sergiu Hart & Andreu Mas-Colell, 1999. "A general class of adaptative strategies," Economics Working Papers 373, Department of Economics and Business, Universitat Pompeu Fabra.
  16. 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.
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