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General procedures leading to correlated equilibria

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  • Amotz Cahn
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    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

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    Bibliographic Info

    Article provided by Springer in its journal International Journal of Games Theory.

    Volume (Year): 33 (2004)
    Issue (Month): 1 (January)
    Pages: 21-40

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    Handle: RePEc:spr:jogath:v:33:y:2004:i:1:p:21-40

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    Web page: http://link.springer.de/link/service/journals/00182/index.htm

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    Related research

    Keywords: adaptive procedures; correlated equilibrium; regret-matching; adaptive heuristics; fictitious play;

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    Cited by:
    1. Sergiu Hart & Yishay Mansour, 2006. "The Communication Complexity of Uncoupled Nash Equilibrium Procedures," Discussion Paper Series dp419, The Center for the Study of Rationality, Hebrew University, Jerusalem.
    2. Dean P Foster & Peyton Young, 2006. "Regret Testing Leads to Nash Equilibrium," Levine's Working Paper Archive 784828000000000676, David K. Levine.
    3. Fabrizio Germano & Gábor Lugosi, 2004. "Global Nash convergence of Foster and Young's regret testing," Economics Working Papers 788, Department of Economics and Business, Universitat Pompeu Fabra.
    4. Hart, Sergiu & Mansour, Yishay, 2010. "How long to equilibrium? The communication complexity of uncoupled equilibrium procedures," Games and Economic Behavior, Elsevier, vol. 69(1), pages 107-126, May.

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