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Beliefs in Repeated Games


  • John H. Nachbar


Consider a two-player discounted infinitely repeated game. A player's belief is a probability distribution over the opponent's repeated game strategies. This paper shows that, for a large class of repeated games, there are no beliefs that satisfy three properties: learnability, a diversity of belief condition called CSP, and consistency. Loosely, if players learn to forecast the path of play whenever each plays a strategy that the other anticipates (in the sense of being in the support of that player's belief) and if the sets of anticipated strategies are sufficiently rich, then neither anticipates any of his opponent's best responses. This generalizes results in Nachbar (1997). Copyright The Econometric Society 2005.

Suggested Citation

  • John H. Nachbar, 2005. "Beliefs in Repeated Games," Econometrica, Econometric Society, vol. 73(2), pages 459-480, March.
  • Handle: RePEc:ecm:emetrp:v:73:y:2005:i:2:p:459-480

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    References listed on IDEAS

    1. Jackson, Matthew O. & Kalai, Ehud, 1997. "Social Learning in Recurring Games," Games and Economic Behavior, Elsevier, vol. 21(1-2), pages 102-134, October.
    2. John H. Nachbar, 1997. "Prediction, Optimization, and Learning in Repeated Games," Econometrica, Econometric Society, vol. 65(2), pages 275-310, March.
    3. Jordan, J. S., 1991. "Bayesian learning in normal form games," Games and Economic Behavior, Elsevier, vol. 3(1), pages 60-81, February.
    4. Kalai, Ehud & Lehrer, Ehud, 1994. "Weak and strong merging of opinions," Journal of Mathematical Economics, Elsevier, vol. 23(1), pages 73-86, January.
    5. 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.
    6. Kalai, Ehud & Lehrer, Ehud, 1993. "Subjective Equilibrium in Repeated Games," Econometrica, Econometric Society, vol. 61(5), pages 1231-1240, September.
    7. Jordan J. S., 1995. "Bayesian Learning in Repeated Games," Games and Economic Behavior, Elsevier, vol. 9(1), pages 8-20, April.
    8. Young, H Peyton, 1993. "The Evolution of Conventions," Econometrica, Econometric Society, vol. 61(1), pages 57-84, January.
    9. Binmore, Ken, 1987. "Modeling Rational Players: Part I," Economics and Philosophy, Cambridge University Press, vol. 3(02), pages 179-214, October.
    10. 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.
    11. 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.
    12. John H. Nachbar, 2001. "Bayesian learning in repeated games of incomplete information," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 18(2), pages 303-326.
    13. 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.
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    Cited by:

    1. Al-Suwailem, Sami, 2014. "Complexity and endogenous instability," Research in International Business and Finance, Elsevier, vol. 30(C), pages 393-410.
    2. Norman, Thomas W.L., 2015. "Learning, hypothesis testing, and rational-expectations equilibrium," Games and Economic Behavior, Elsevier, vol. 90(C), pages 93-105.
    3. Burkhard Schipper, 2015. "Strategic teaching and learning in games," Working Papers 151, University of California, Davis, Department of Economics.
    4. Sami Al-Suwailem, 2012. "Complexity and Endogenous Instability," ASSRU Discussion Papers 1203, ASSRU - Algorithmic Social Science Research Unit.
    5. Leoni Patrick L, 2009. "A Constructive Proof that Learning in Repeated Games Leads to Nash Equilibria," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 8(1), pages 1-20, January.
    6. Dean P Foster & Peyton Young, 2006. "Regret Testing Leads to Nash Equilibrium," Levine's Working Paper Archive 784828000000000676, David K. Levine.

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