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A General Class Of Adaptive Strategies

In: Simple Adaptive Strategies From Regret-Matching to Uncoupled Dynamics

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Listed:
  • Sergiu Hart
  • Andreu Mas-Colell

Abstract

We exhibit and characterize an entire class of simple adaptive strategies, in the repeated play of a game, having the Hannan-consistency property: in the long run, the player is guaranteed an average payoff as large as the best-reply payoff to the empirical distribution of play of the other players; i.e., there is no “regret.” Smooth fictitious play (Fudenberg and Levine 1995) and regret matching (Hart and Mas-Colell 2000) are particular cases. The motivation and application of the current paper come from the study of procedures whose empirical distribution of play is, in the long run, (almost) a correlated equilibrium. For the analysis we first develop a generalization of Blackwell's (1956) approachability strategy for games with vector payoffs.

Suggested Citation

  • Sergiu Hart & Andreu Mas-Colell, 2013. "A General Class Of Adaptive Strategies," World Scientific Book Chapters, in: Simple Adaptive Strategies From Regret-Matching to Uncoupled Dynamics, chapter 3, pages 47-76, World Scientific Publishing Co. Pte. Ltd..
  • Handle: RePEc:wsi:wschap:9789814390705_0003
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    References listed on IDEAS

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    1. Fudenberg, Drew & Levine, David, 1998. "Learning in games," European Economic Review, Elsevier, vol. 42(3-5), pages 631-639, May.
    2. 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.
    3. 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.
    4. Sergiu Hart & Andreu Mas-Colell, 2013. "A Simple Adaptive Procedure Leading To Correlated Equilibrium," World Scientific Book Chapters, in: Simple Adaptive Strategies From Regret-Matching to Uncoupled Dynamics, chapter 2, pages 17-46, World Scientific Publishing Co. Pte. Ltd..
    5. Fudenberg, Drew & Levine, David K., 1999. "Conditional Universal Consistency," Games and Economic Behavior, Elsevier, vol. 29(1-2), pages 104-130, October.
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    12. Foster, Dean P. & Vohra, Rakesh V., 1997. "Calibrated Learning and Correlated Equilibrium," Games and Economic Behavior, Elsevier, vol. 21(1-2), pages 40-55, October.
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    More about this item

    Keywords

    Game Theory; Dynamics; Equilibrium; Nash Equilibrium; Correlated Equilibrium; Adaptive Dynamics; Simple Strategies; Regret-Based Strategies; Uncoupled Dynamics; Bounded Rationality;
    All these keywords.

    JEL classification:

    • C7 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory
    • D7 - Microeconomics - - Analysis of Collective Decision-Making
    • C6 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling

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