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Almost-Rational Learning of Nash Equilibrium without Absolute Continuity

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  • Thomas Norman

Abstract

If players learn to play an infinitely repeated game using Bayesian learning, it is known that their strategies eventually approximate Nash equilibria of the repeated game under an absolute-continuity assumption on their prior beliefs. We suppose here that Bayesian learners do not start with such a "grain of truth", but with arbitrarily low probability they revise beliefs that are performing badly. We show that this process converges in probability to a Nash equilibrium of the repeated game.

Suggested Citation

  • Thomas Norman, 2012. "Almost-Rational Learning of Nash Equilibrium without Absolute Continuity," Economics Series Working Papers 602, University of Oxford, Department of Economics.
  • Handle: RePEc:oxf:wpaper:602
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    File URL: https://ora.ox.ac.uk/objects/uuid:9019b4e7-4faf-40be-8ab4-ec23e380b2b0
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    References listed on IDEAS

    as
    1. John H. Nachbar, 1997. "Prediction, Optimization, and Learning in Repeated Games," Econometrica, Econometric Society, vol. 65(2), pages 275-310, March.
    2. Ehud Lehrer & Sylvain Sorin, 1998. "-Consistent equilibrium in repeated games," International Journal of Game Theory, Springer;Game Theory Society, vol. 27(2), pages 231-244.
    3. Kalai, Ehud & Lehrer, Ehud, 1993. "Rational Learning Leads to Nash Equilibrium," Econometrica, Econometric Society, vol. 61(5), pages 1019-1045, September.
    4. Dean Foster & H Peyton Young, 1999. "On the Impossibility of Predicting the Behavior of Rational Agents," Economics Working Paper Archive 423, The Johns Hopkins University,Department of Economics, revised Jun 2001.
    5. Sandroni, Alvaro, 1998. "Necessary and Sufficient Conditions for Convergence to Nash Equilibrium: The Almost Absolute Continuity Hypothesis," Games and Economic Behavior, Elsevier, vol. 22(1), pages 121-147, January.
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    Cited by:

    1. Levy, Yehuda John, 2015. "Limits to rational learning," Journal of Economic Theory, Elsevier, vol. 160(C), pages 1-23.

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    More about this item

    Keywords

    Repeated games; Nash equilibrium; Rational learning; Bayesian learning; Absolute continuity;
    All these keywords.

    JEL classification:

    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games
    • D83 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Search; Learning; Information and Knowledge; Communication; Belief; Unawareness

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