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The possibility of Bayesian learning in repeated games

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  • Norman, Thomas W.L.

Abstract

In infinitely repeated games, Nachbar (1997, 2005) has shown that Bayesian learning of a restricted strategy set is inconsistent; the beliefs required to learn any element of such a set will lead best responses to lie outside of it in most games. But I establish here that Nash convergence of Bayesian learning requires only that optimal play (rather than any possible play) is learnable, and an appropriately modified notion of learnability is consistent in many of the games to which Nachbar's result applies. This means that rational learning of equilibrium is possible in an important class including coordination games, which I illustrate with two examples of positive learning results.

Suggested Citation

  • Norman, Thomas W.L., 2022. "The possibility of Bayesian learning in repeated games," Games and Economic Behavior, Elsevier, vol. 136(C), pages 142-152.
    • Handle: RePEc:eee:gamebe:v:136:y:2022:i:c:p:142-152
    DOI: 10.1016/j.geb.2022.09.002
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    References listed on IDEAS

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    1. Ignacio Esponda & Demian Pouzo, 2016. "Berk–Nash Equilibrium: A Framework for Modeling Agents With Misspecified Models," Econometrica, Econometric Society, vol. 84, pages 1093-1130, May.
    2. John H. Nachbar, 1997. "Prediction, Optimization, and Learning in Repeated Games," Econometrica, Econometric Society, vol. 65(2), pages 275-310, March.
    3. 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.
    4. ,, 2015. "Merging with a set of probability measures: a characterization," Theoretical Economics, Econometric Society, vol. 10(2), May.
    5. Kalai, Ehud & Lehrer, Ehud, 1994. "Weak and strong merging of opinions," Journal of Mathematical Economics, Elsevier, vol. 23(1), pages 73-86, January.
    6. Sandroni, Alvaro, 2000. "Reciprocity and Cooperation in Repeated Coordination Games: The Principled-Player Approach," Games and Economic Behavior, Elsevier, vol. 32(2), pages 157-182, August.
    7. Foster, Dean P. & Young, H. Peyton, 2003. "Learning, hypothesis testing, and Nash equilibrium," Games and Economic Behavior, Elsevier, vol. 45(1), pages 73-96, October.
    8. Kalai, Ehud & Stanford, William, 1988. "Finite Rationality and Interpersonal Complexity in Repeated Games," Econometrica, Econometric Society, vol. 56(2), pages 397-410, March.
    9. Fudenberg, Drew & Levine, David K, 1993. "Self-Confirming Equilibrium," Econometrica, Econometric Society, vol. 61(3), pages 523-545, May.
    10. Kalai, Ehud & Lehrer, Ehud, 1993. "Rational Learning Leads to Nash Equilibrium," Econometrica, Econometric Society, vol. 61(5), pages 1019-1045, September.
    11. Levy, Yehuda John, 2015. "Limits to rational learning," Journal of Economic Theory, Elsevier, vol. 160(C), pages 1-23.
    12. 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.
    13. John H. Nachbar, 2005. "Beliefs in Repeated Games," Econometrica, Econometric Society, vol. 73(2), pages 459-480, March.
    14. Stahl Dale O., 1993. "Evolution of Smartn Players," Games and Economic Behavior, Elsevier, vol. 5(4), pages 604-617, October.
    15. 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.
    16. Kalai, Ehud & Lehrer, Ehud, 1993. "Subjective Equilibrium in Repeated Games," Econometrica, Econometric Society, vol. 61(5), pages 1231-1240, September.
    17. Ehud Lehrer & Rann Smorodinsky, 1996. "Compatible Measures and Merging," Mathematics of Operations Research, INFORMS, vol. 21(3), pages 697-706, August.
    18. Yuichi Noguchi, 2015. "Bayesian Learning, Smooth Approximate Optimal Behavior, and Convergence to ε‐Nash Equilibrium," Econometrica, Econometric Society, vol. 83, pages 353-373, January.
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    More about this item

    Keywords

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

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • 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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