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Bayesian Learning Leads to Correlated Equilibria in Normal Form Games

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  • Nyarko, Yaw

Abstract

Consider an infinitely repeated normal form game where each player is characterized by a "type" which may be unknown to the other players of the game. Impose only two conditions on the behavior of the players. First, impose the Savage (1954) axioms; i.e., each player has some beliefs about the evolution of the game and maximizes its expected payoffs at each date given those beliefs. Second, suppose that any event which has probability zero under one player's beliefs also has probability zero under the other player's beliefs. We show that under these two conditions limit points of beliefs and of the empirical distributions (i.e., sample path averages or histograms) are correlated equilibria of the "true" game (i.e., the game characterized by the true vector of types).

Suggested Citation

  • Nyarko, Yaw, 1994. "Bayesian Learning Leads to Correlated Equilibria in Normal Form Games," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 4(6), pages 821-841, October.
  • Handle: RePEc:spr:joecth:v:4:y:1994:i:6:p:821-41
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    Cited by:

    1. Lehrer, Ehud & Smorodinsky, Rann, 2000. "Relative entropy in sequential decision problems1," Journal of Mathematical Economics, Elsevier, vol. 33(4), pages 425-439, May.
    2. 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.
    3. Lehrer, Ehud & Smorodinsky, Rann, 1997. "Repeated Large Games with Incomplete Information," Games and Economic Behavior, Elsevier, vol. 18(1), pages 116-134, January.
    4. Yoo, Seung Han, 2014. "Learning a population distribution," Journal of Economic Dynamics and Control, Elsevier, vol. 48(C), pages 188-201.
    5. Dean Foster & Peyton Young, "undated". "Learning with Hazy Beliefs," ELSE working papers 023, ESRC Centre on Economics Learning and Social Evolution.
    6. Nyarko, Yaw, 1997. "Convergence in Economic Models with Bayesian Hierarchies of Beliefs," Journal of Economic Theory, Elsevier, vol. 74(2), pages 266-296, June.
    7. Mario Gilli, 2002. "Rational Learning in Imperfect Monitoring Games," Working Papers 46, University of Milano-Bicocca, Department of Economics, revised Mar 2002.
    8. Müller, Stephan, 2014. "The evolution of inequality aversion in a simplified game of life," Center for European, Governance and Economic Development Research Discussion Papers 219, University of Goettingen, Department of Economics.
    9. Matthew O. Jackson & Ehud Kalai, 1997. "False Reputation in a Society of Players," Discussion Papers 1184R, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    10. Aoyagi, Masaki, 1998. "Mutual Observability and the Convergence of Actions in a Multi-Person Two-Armed Bandit Model," Journal of Economic Theory, Elsevier, vol. 82(2), pages 405-424, October.
    11. Turdaliev, Nurlan, 2002. "Calibration and Bayesian learning," Games and Economic Behavior, Elsevier, vol. 41(1), pages 103-119, October.
    12. Jackson, Matthew O. & Kalai, Ehud, 1999. "Reputation versus Social Learning," Journal of Economic Theory, Elsevier, vol. 88(1), pages 40-59, September.

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