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A Simple Adaptive Procedure Leading to Correlated Equilibrium

Author

Listed:
  • 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).

Suggested Citation

  • Sergiu Hart & Andreu Mas-Colell, 1997. "A Simple Adaptive Procedure Leading to Correlated Equilibrium," Game Theory and Information 9703006, University Library of Munich, Germany, revised 25 Nov 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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    References listed on IDEAS

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    5. 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.
    6. Hart, Sergiu & Mas-Colell, Andreu, 2001. "A General Class of Adaptive Strategies," Journal of Economic Theory, Elsevier, vol. 98(1), pages 26-54, May.
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    12. 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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    More about this item

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • D83 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Search; Learning; Information and Knowledge; Communication; Belief; Unawareness

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