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Limits to rational learning

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  • Levy, Yehuda John

Abstract

A long-standing open question raised in the seminal paper of Kalai and Lehrer (1993) is whether or not the play of a repeated game, in the rational learning model introduced there, must eventually resemble the play of exact equilibria, and not just the play of approximate equilibria as demonstrated there. This paper shows that play may remain distant – in fact, mutually singular – from the play of any equilibrium of the repeated game. We further show that the same inaccessibility holds in Bayesian games, where the play of a Bayesian equilibrium may continue to remain distant from the play of any equilibrium of the true game.

Suggested Citation

  • Levy, Yehuda John, 2015. "Limits to rational learning," Journal of Economic Theory, Elsevier, vol. 160(C), pages 1-23.
    • Handle: RePEc:eee:jetheo:v:160:y:2015:i:c:p:1-23
    DOI: 10.1016/j.jet.2015.08.001
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    1. Kalai, Ehud & Lehrer, Ehud, 1993. "Rational Learning Leads to Nash Equilibrium," Econometrica, Econometric Society, vol. 61(5), pages 1019-1045, September.
    2. Jordan, J. S., 1991. "Bayesian learning in normal form games," Games and Economic Behavior, Elsevier, vol. 3(1), pages 60-81, February.
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    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.
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    6. Kalai, Ehud & Lehrer, Ehud, 1995. "Subjective games and equilibria," Games and Economic Behavior, Elsevier, vol. 8(1), pages 123-163.
    7. Gilli, Mario, 2001. "A General Approach to Rational Learning in Games," Bulletin of Economic Research, Wiley Blackwell, vol. 53(4), pages 275-303, October.
    8. Ehud Lehrer & Rann Smorodinsky, 1996. "Compatible Measures and Merging," Mathematics of Operations Research, INFORMS, vol. 21(3), pages 697-706, August.
    9. Matthew O. Jackson & Ehud Kalai & Rann Smorodinsky, 1999. "Bayesian Representation of Stochastic Processes under Learning: de Finetti Revisited," Econometrica, Econometric Society, vol. 67(4), pages 875-894, July.
    10. Yaw Nyarko, 1998. "Bayesian learning and convergence to Nash equilibria without common priors," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 11(3), pages 643-655.
    11. Thomas D. Jeitschko, 1998. "Learning in Sequential Auctions," Southern Economic Journal, John Wiley & Sons, vol. 65(1), pages 98-112, July.
    12. Miller, Ronald I. & Sanchirico, Chris William, 1999. "The Role of Absolute Continuity in "Merging of Opinions" and "Rational Learning"," Games and Economic Behavior, Elsevier, vol. 29(1-2), pages 170-190, October.
    13. Ronald Miller & Chris Sanchirico, "undated". "Almost Everybody Disagrees Almost All the Time: The Genericity of Weakly Merging Nowhere," Scholarship at Penn Law upenn_wps-1001, University of Pennsylvania Law School.
    14. 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.
    15. Thomas Norman, 2012. "Almost-Rational Learning of Nash Equilibrium without Absolute Continuity," Economics Series Working Papers 602, University of Oxford, Department of Economics.
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    Cited by:

    1. Norman, Thomas W.L., 2022. "The possibility of Bayesian learning in repeated games," Games and Economic Behavior, Elsevier, vol. 136(C), pages 142-152.

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    More about this item

    Keywords

    Rational learning; Repeated games; Nash equilibrium;
    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
    • C65 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Miscellaneous Mathematical Tools

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