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Beliefs in Repeated Games

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  • John H. Nachbar

Abstract

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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    File URL: http://hdl.handle.net/10.1111/j.1468-0262.2005.00585.x
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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. Al-Suwailem, Sami, 2014. "Complexity and endogenous instability," Research in International Business and Finance, Elsevier, vol. 30(C), pages 393-410.
    3. Burkhard C. Schipper, 2022. "Strategic Teaching and Learning in Games," American Economic Journal: Microeconomics, American Economic Association, vol. 14(3), pages 321-352, August.
    4. Jindani, Sam, 2022. "Learning efficient equilibria in repeated games," Journal of Economic Theory, Elsevier, vol. 205(C).
    5. Chernov, G. & Susin, I., 2019. "Models of learning in games: An overview," Journal of the New Economic Association, New Economic Association, vol. 44(4), pages 77-125.
    6. Norman, Thomas W.L., 2015. "Learning, hypothesis testing, and rational-expectations equilibrium," Games and Economic Behavior, Elsevier, vol. 90(C), pages 93-105.
    7. Scott E. Page, 2008. "Uncertainty, Difficulty, and Complexity," Journal of Theoretical Politics, , vol. 20(2), pages 115-149, April.
    8. 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.
    9. Tsionas, Mike G., 2023. "Bayesian learning in performance. Is there any?," European Journal of Operational Research, Elsevier, vol. 311(1), pages 263-282.
    10. Dean P Foster & Peyton Young, 2006. "Regret Testing Leads to Nash Equilibrium," Levine's Working Paper Archive 784828000000000676, David K. Levine.
    11. Mathevet, Laurent, 2018. "An axiomatization of plays in repeated games," Games and Economic Behavior, Elsevier, vol. 110(C), pages 19-31.
    12. Burkhard Schipper, 2015. "Strategic teaching and learning in games," Working Papers 151, University of California, Davis, Department of Economics.
    13. Sami Al-Suwailem, 2012. "Complexity and Endogenous Instability," ASSRU Discussion Papers 1203, ASSRU - Algorithmic Social Science Research Unit.
    14. Pierpaolo Battigalli & Davide Bordoli, 2025. "Sophisticated reasoning, learning, and equilibrium in repeated games with imperfect feedback," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 80(2), pages 421-464, September.

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