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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 conditions, learnability, consistency, and a diversity condition, CS. This impossibility theorem generalizes results in Nachbar (1997).

Suggested Citation

  • John H. Nachbar, 2003. "Beliefs in Repeated Games," ISER Discussion Paper 0597, Institute of Social and Economic Research, Osaka University.
    • Handle: RePEc:dpr:wpaper:0597
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    File URL: https://www.iser.osaka-u.ac.jp/library/dp/2003/DP0597.pdf
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    Cited by:

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    2. Norman, Thomas W.L., 2022. "The possibility of Bayesian learning in repeated games," Games and Economic Behavior, Elsevier, vol. 136(C), pages 142-152.
    3. Burkhard Schipper, 2015. "Strategic teaching and learning in games," Working Papers 151, University of California, Davis, Department of Economics.
    4. Al-Suwailem, Sami, 2014. "Complexity and endogenous instability," Research in International Business and Finance, Elsevier, vol. 30(C), pages 393-410.
    5. Jindani, Sam, 2022. "Learning efficient equilibria in repeated games," Journal of Economic Theory, Elsevier, vol. 205(C).
    6. 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.
    7. Norman, Thomas W.L., 2015. "Learning, hypothesis testing, and rational-expectations equilibrium," Games and Economic Behavior, Elsevier, vol. 90(C), pages 93-105.
    8. Sami Al-Suwailem, 2012. "Complexity and Endogenous Instability," ASSRU Discussion Papers 1203, ASSRU - Algorithmic Social Science Research Unit.
    9. Scott E. Page, 2008. "Uncertainty, Difficulty, and Complexity," Journal of Theoretical Politics, , vol. 20(2), pages 115-149, April.
    10. 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.
    11. Tsionas, Mike G., 2023. "Bayesian learning in performance. Is there any?," European Journal of Operational Research, Elsevier, vol. 311(1), pages 263-282.
    12. Dean P Foster & Peyton Young, 2006. "Regret Testing Leads to Nash Equilibrium," Levine's Working Paper Archive 784828000000000676, David K. Levine.
    13. Mathevet, Laurent, 2018. "An axiomatization of plays in repeated games," Games and Economic Behavior, Elsevier, vol. 110(C), pages 19-31.

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