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A Simple Adaptive Procedure Leading to Correlated Equilibrium

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Author Info
Sergiu Hart
Andreu Mas-Colell ()

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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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File URL: http://www.econ.upf.edu/docs/papers/downloads/200.ps.gz
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Publisher Info
Paper provided by Department of Economics and Business, Universitat Pompeu Fabra in its series Economics Working Papers with number 200.

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Date of creation: Mar 1996
Date of revision: Dec 1996
Handle: RePEc:upf:upfgen:200

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Related research
Keywords: Correlated equilibrium; Nash equilibrium; adaptive prodedure; regret; Blackwell approachability;

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Find related papers by JEL classification:
C70 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - General
C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games

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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. [Downloadable!] (restricted)
  2. Sanchirico, Chris William, 1996. "A Probabilistic Model of Learning in Games," Econometrica, Econometric Society, vol. 64(6), pages 1375-93, November. [Downloadable!] (restricted)
    Other versions:
  3. Aumann, Robert J., 1974. "Subjectivity and correlation in randomized strategies," Journal of Mathematical Economics, Elsevier, vol. 1(1), pages 67-96, March. [Downloadable!] (restricted)
  4. 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. [Downloadable!] (restricted)
  5. Colin Camerer & Teck-Hua Ho, 1999. "Experience-weighted Attraction Learning in Normal Form Games," Econometrica, Econometric Society, vol. 67(4), pages 827-874, July.
  6. Mertens, J.-F., 1986. "Repeated games," CORE Discussion Papers 1986024, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  7. Nau, Robert F. & McCardle, Kevin F., 1990. "Coherent behavior in noncooperative games," Journal of Economic Theory, Elsevier, vol. 50(2), pages 424-444, April. [Downloadable!] (restricted)
  8. 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. [Downloadable!] (restricted)
  9. Fudenberg, Drew & Levine, David, 1998. "Learning in games," European Economic Review, Elsevier, vol. 42(3-5), pages 631-639, May. [Downloadable!] (restricted)
  10. Fudenberg, Drew & Levine, David K., 1999. "Conditional Universal Consistency," Games and Economic Behavior, Elsevier, vol. 29(1-2), pages 104-130, October. [Downloadable!] (restricted)
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  11. Camerer, Colin & Ho, Teck-Hua, 1997. "Experience-Weighted Attraction Learning in Games: A Unifying Approach," Working Papers 1003, California Institute of Technology, Division of the Humanities and Social Sciences. [Downloadable!]
  12. 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. [Downloadable!] (restricted)
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  13. Roger B. Myerson, 1995. "Dual Reduction and Elementary Games," Discussion Papers 1133, Northwestern University, Center for Mathematical Studies in Economics and Management Science. [Downloadable!]
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  14. 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. [Downloadable!]
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