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Bayesian learning in repeated games of incomplete information


  • John H. Nachbar

    () (Department of Economics, Washington University, One Brookings Drive, St. Louis, MO 63130, USA)


In Nachbar [20] and, more definitively, Nachbar [22], I argued that, for a large class of discounted infinitely repeated games of complete information (i.e. stage game payoff functions are common knowledge), it is impossible to construct a Bayesian learning theory in which player beliefs are simultaneously weakly cautious, symmetric, and consistent. The present paper establishes a similar impossibility theorem for repeated games of incomplete information, that is, for repeated games in which stage game payoff functions are private information.

Suggested Citation

  • 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.
  • Handle: RePEc:spr:sochwe:v:18:y:2001:i:2:p:303-326
    Note: Received: 15 October 1997/Accepted: 17 March 1999

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    References listed on IDEAS

    1. Atkinson, Anthony B, 2001. "The Strange Disappearance of Welfare Economics," Kyklos, Wiley Blackwell, vol. 54(2-3), pages 193-206.
    2. I. M. D. Little, 1952. "Social Choice and Individual Values," Journal of Political Economy, University of Chicago Press, vol. 60, pages 422-422.
    3. Sen, Amartya, 1992. "Minimal Liberty," Economica, London School of Economics and Political Science, vol. 59(234), pages 139-159, May.
    4. Kemp, Murray C & Ng, Yew-Kwang, 1976. "On the Existence of Social Welfare Functions, Social Orderings and Social Decision Functions," Economica, London School of Economics and Political Science, vol. 43(169), pages 59-66, February.
    5. Cohen, Jon S. & Weitzman, Martin L., 1975. "A Marxian model of enclosures," Journal of Development Economics, Elsevier, vol. 1(4), pages 287-336, November.
    6. Sen, Amartya, 1995. "Rationality and Social Choice," American Economic Review, American Economic Association, vol. 85(1), pages 1-24, March.
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    Cited by:

    1. 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.
    2. Young, H. Peyton, 2002. "On the limits to rational learning," European Economic Review, Elsevier, vol. 46(4-5), pages 791-799, May.
    3. Norman, Thomas W.L., 2015. "Learning, hypothesis testing, and rational-expectations equilibrium," Games and Economic Behavior, Elsevier, vol. 90(C), pages 93-105.
    4. 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.
    5. Burkhard Schipper, 2015. "Strategic teaching and learning in games," Working Papers 151, University of California, Davis, Department of Economics.
    6. John H. Nachbar, 2005. "Beliefs in Repeated Games," Econometrica, Econometric Society, vol. 73(2), pages 459-480, March.

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