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Prediction, Optimization, and Learning in Repeated Games

Author

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  • John H. Nachbar

    (Washington University, St. Louis)

Abstract

Consider a two-player discounted repeated game in which each player optimizes with respect to prior beliefs about his opponent's repeated game strategy. One would like to argue that if beliefs are cautious then players will learn as the game unfolds to predict the continuation path of play. If this conjecture were true then a convergence result due to Kalai and Lehrer would imply that the continuation path would asymptotically resemble the path of a Nash equilibrium. One would thus have constructed a theory which predicts Nash equilibrium as the necessary long-run consequence of optimization by cautious players. This paper points out that there is an obstacle to such a result in the form of a potential conflict between prediction and optimization.

Suggested Citation

  • John H. Nachbar, 1995. "Prediction, Optimization, and Learning in Repeated Games," Game Theory and Information 9504001, University Library of Munich, Germany, revised 22 Feb 1996.
  • Handle: RePEc:wpa:wuwpga:9504001
    Note: Postscript from AMS-LaTeX, 46 pages
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    References listed on IDEAS

    as
    1. Kalai, Ehud & Stanford, William, 1988. "Finite Rationality and Interpersonal Complexity in Repeated Games," Econometrica, Econometric Society, vol. 56(2), pages 397-410, March.
    2. Binmore, Ken, 1987. "Modeling Rational Players: Part I," Economics and Philosophy, Cambridge University Press, vol. 3(02), pages 179-214, October.
    3. Lawrence Blume & David Easley, 1993. "Rational Expectations and Rational Learning," Game Theory and Information 9307003, University Library of Munich, Germany.
    Full references (including those not matched with items on IDEAS)

    More about this item

    Keywords

    Repeated games; rational learning; Bayesian learning.;

    JEL classification:

    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games

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