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A General Class of Adaptive Strategies

Author

Listed:
  • Sergiu Hart

    (The Hebrew University of Jerusalem, Israel)

  • Andreu Mas-Colell

    (Universitat Pompeu Fabra, Barcelona, Spain)

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 [1956a] approachability strategy for games with vector payoffs.

Suggested Citation

  • Sergiu Hart & Andreu Mas-Colell, 1999. "A General Class of Adaptive Strategies," Game Theory and Information 9904001, EconWPA, revised 23 Mar 2000.
  • Handle: RePEc:wpa:wuwpga:9904001
    Note: Type of Document - Scientific Word v.2.5. First version: March 1999. Revised: December 1999.
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    References listed on IDEAS

    as
    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. D. Foster & R. Vohra, 2010. "Regret in the On-line Decision Problem," Levine's Working Paper Archive 569, David K. Levine.
    4. Fudenberg, Drew & Levine, David K., 1999. "Conditional Universal Consistency," Games and Economic Behavior, Elsevier, vol. 29(1-2), pages 104-130, October.
    5. 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.
    6. Sergiu Hart & Andreu Mas-Colell, 2000. "A Simple Adaptive Procedure Leading to Correlated Equilibrium," Econometrica, Econometric Society, vol. 68(5), pages 1127-1150, September.
    7. Monderer, Dov & Samet, Dov & Sela, Aner, 1997. "Belief Affirming in Learning Processes," Journal of Economic Theory, Elsevier, vol. 73(2), pages 438-452, April.
    8. D. Blackwell, 2010. "Controlled Random Walks," Levine's Working Paper Archive 465, David K. Levine.
    9. 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.
    10. D. Blackwell, 2010. "An Analog of the Minmax Theorem for Vector Payoffs," Levine's Working Paper Archive 466, David K. Levine.
    11. D. Foster & R. Vohra, 2010. "Calibrated Learning and Correlated Equilibrium," Levine's Working Paper Archive 568, David K. Levine.
    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.
    13. J. Robinson, 1969. "An Iterative Method of Solving a Game," Levine's Working Paper Archive 422, David K. Levine.
    14. N. Littlestone & M. Warmuth, 2010. "The Weighted Majority Algorithm," Levine's Working Paper Archive 575, David K. Levine.
    15. Freund, Yoav & Schapire, Robert E., 1999. "Adaptive Game Playing Using Multiplicative Weights," Games and Economic Behavior, Elsevier, vol. 29(1-2), pages 79-103, October.
    16. D. Foster & R. Vohra, 2010. "Asymptotic Calibration," Levine's Working Paper Archive 468, David K. Levine.
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    More about this item

    Keywords

    adaptive strategies; approachability; correlated equilibrium; fictitious play; regret;

    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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