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Bayesian learning and convergence to Nash equilibria without common priors

Author

Listed:
  • Yaw Nyarko

    (Department of Economics, New York University, 269 Mercer Street, New York, NY10003, USA)

Abstract

Consider an infinitely repeated game where each player is characterized by a "type" which may be unknown to the other players in the game. Suppose further that each player's belief about others is independent of that player's type. Impose an absolute continuity condition on the ex ante beliefs of players (weaker than mutual absolute continuity). Then any limit point of beliefs of players about the future of the game conditional on the past lies in the set of Nash or Subjective equilibria. Our assumption does not require common priors so is weaker than Jordan (1991); however our conclusion is weaker, we obtain convergence to subjective and not necessarily Nash equilibria. Our model is a generalization of the Kalai and Lehrer (1993) model. Our assumption is weaker than theirs. However, our conclusion is also weaker, and shows that limit points of beliefs, and not actual play, are subjective equilibria.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:joecth:v:11:y:1998:i:3:p:643-655
    Note: Received: March 3, 1995; revised version: February 17, 1997
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    Citations

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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.
    2. Matthew O. Jackson & Ehud Kalai & Rann Smorodinsky, 1997. "Patterns, Types, and Bayesian Learning," Game Theory and Information 9711002, University Library of Munich, Germany.
    3. Kelly, David L. & Shorish, Jamsheed, 2000. "Stability of Functional Rational Expectations Equilibria," Journal of Economic Theory, Elsevier, vol. 95(2), pages 215-250, December.
    4. Jindani, Sam, 2022. "Learning efficient equilibria in repeated games," Journal of Economic Theory, Elsevier, vol. 205(C).
    5. Yoo, Seung Han, 2014. "Learning a population distribution," Journal of Economic Dynamics and Control, Elsevier, vol. 48(C), pages 188-201.
    6. Levy, Yehuda John, 2015. "Limits to rational learning," Journal of Economic Theory, Elsevier, vol. 160(C), pages 1-23.
    7. 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.
    8. Mario Gilli, 2002. "Rational Learning in Imperfect Monitoring Games," Working Papers 46, University of Milano-Bicocca, Department of Economics, revised Mar 2002.
    9. John H. Nachbar, 2005. "Beliefs in Repeated Games," Econometrica, Econometric Society, vol. 73(2), pages 459-480, March.
    10. Gregory Price, 2008. "NEA Presidential Address: Black Economists of the World You Cite!!," The Review of Black Political Economy, Springer;National Economic Association, vol. 35(1), pages 1-12, March.
    11. Young, H. Peyton, 2002. "On the limits to rational learning," European Economic Review, Elsevier, vol. 46(4-5), pages 791-799, May.
    12. Funai, Naoki, 2022. "Reinforcement learning with foregone payoff information in normal form games," Journal of Economic Behavior & Organization, Elsevier, vol. 200(C), pages 638-660.

    More about this item

    JEL classification:

    • C70 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - General
    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games
    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design
    • D83 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Search; Learning; Information and Knowledge; Communication; Belief; Unawareness
    • D84 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Expectations; Speculations

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