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General procedures leading to correlated equilibria

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  • Amotz Cahn

Abstract

Hart and Mas-Colell [2000] show that if all players play “regret-matching” strategies, i.e., they play with probabilities proportional to the regrets, then the empirical distribution of play converges to the set of correlated equilibria, and the regrets of every player converge to zero. Here we show that if only one player, say player i, plays with these probabilities, while the other players are “not too sophisticated,” then the result that player i’s regrets converge to zero continues to hold. The condition of “not too sophisticated” essentially says that the effect of one change of action of player i on the future actions of the other players decreases to zero as the horizon goes to infinity. Furthermore, we generalize all these results to a whole class of “regret-based” strategies introduced in Hart and Mas-Colell [2001]. In particular, these simplify the “conditional smooth fictitious play” of Fudenberg and Levine [1999]. Copyright Springer-Verlag 2004

Suggested Citation

  • Amotz Cahn, 2004. "General procedures leading to correlated equilibria," International Journal of Game Theory, Springer;Game Theory Society, vol. 33(1), pages 21-40, January.
    • Handle: RePEc:spr:jogath:v:33:y:2004:i:1:p:21-40
    DOI: 10.1007/s001820400182
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    Cited by:

    1. Sergiu Hart & Yishay Mansour, 2006. "The Communication Complexity of Uncoupled Nash Equilibrium Procedures," Levine's Bibliography 122247000000001299, UCLA Department of Economics.
    2. Germano, Fabrizio & Lugosi, Gabor, 2007. "Global Nash convergence of Foster and Young's regret testing," Games and Economic Behavior, Elsevier, vol. 60(1), pages 135-154, July.
    3. Dean P Foster & Peyton Young, 2006. "Regret Testing Leads to Nash Equilibrium," Levine's Working Paper Archive 784828000000000676, David K. Levine.
    4. Michel Benaïm & Josef Hofbauer & Sylvain Sorin, 2006. "Stochastic Approximations and Differential Inclusions, Part II: Applications," Mathematics of Operations Research, INFORMS, vol. 31(4), pages 673-695, November.
    5. Sergiu Hart & Yishay Mansour, 2013. "How Long To Equilibrium? The Communication Complexity Of Uncoupled Equilibrium Procedures," World Scientific Book Chapters, in: Simple Adaptive Strategies From Regret-Matching to Uncoupled Dynamics, chapter 10, pages 215-249, World Scientific Publishing Co. Pte. Ltd..

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