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Rational Learning Leads to Nash Equilibrium

  • Kalai, Ehud
  • Lehrer, Ehud

Subjective utility maximizers, in an infinitely repeated game, will learn to predict opponents' future strategies and will converge to play according to a Nash equilibrium of the repeated game. Players' initial uncertainty is placed directly on opponents' strategies and the above result is obtained under the assumption that the individual beliefs are compatible with the chosen strategies. An immediate corollary is that, when playing a Harsanyi-Nash equilibrium of a repeated game of incomplete information about opponents' payoff matrices, players will eventually play a Nash equilibrium of the real game, as if they had complete information. Copyright 1993 by The Econometric Society.

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Article provided by Econometric Society in its journal Econometrica.

Volume (Year): 61 (1993)
Issue (Month): 5 (September)
Pages: 1019-45

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Handle: RePEc:ecm:emetrp:v:61:y:1993:i:5:p:1019-45
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  1. Fudenberg, Drew & Levine, David K, 1993. "Steady State Learning and Nash Equilibrium," Econometrica, Econometric Society, vol. 61(3), pages 547-73, May.
  2. Aumann, Robert J. & Heifetz, Aviad, 2001. "Incomplete Information," Working Papers 1124, California Institute of Technology, Division of the Humanities and Social Sciences.
  3. Jordan, J. S., 1992. "The exponential convergence of Bayesian learning in normal form games," Games and Economic Behavior, Elsevier, vol. 4(2), pages 202-217, April.
  4. Pearce, David G, 1984. "Rationalizable Strategic Behavior and the Problem of Perfection," Econometrica, Econometric Society, vol. 52(4), pages 1029-50, July.
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  8. Ehud Kalai & Ehud Lehrer, 1991. "Subjective Equilibrium in Repeated Games," Discussion Papers 981, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
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  14. Drew Fudenberg & David K. Levine, 1993. "Self-Confirming Equilibrium," Levine's Working Paper Archive 2147, David K. Levine.
  15. Mertens,Jean-François & Sorin,Sylvain & Zamir,Shmuel, 2015. "Repeated Games," Cambridge Books, Cambridge University Press, number 9781107030206, 1.
    • Mertens,Jean-François & Sorin,Sylvain & Zamir,Shmuel, 2015. "Repeated Games," Cambridge Books, Cambridge University Press, number 9781107662636, 1.
  16. Blume, L. E. & Bray, M. M. & Easley, D., 1982. "Introduction to the stability of rational expectations equilibrium," Journal of Economic Theory, Elsevier, vol. 26(2), pages 313-317, April.
  17. Rothschild, Michael, 1974. "A two-armed bandit theory of market pricing," Journal of Economic Theory, Elsevier, vol. 9(2), pages 185-202, October.
  18. David Canning, 1989. "Convergence to Equilibrium in a Sequence for Games with Learning," STICERD - Theoretical Economics Paper Series 190, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
  19. Jordan, J. S., 1991. "Bayesian learning in normal form games," Games and Economic Behavior, Elsevier, vol. 3(1), pages 60-81, February.
  20. Jordan, J. S., 1985. "Learning rational expectations: The finite state case," Journal of Economic Theory, Elsevier, vol. 36(2), pages 257-276, August.
  21. Alvin E. Roth & V. Prasnikar & M. Okuno-Fujiwara & S. Zamir, 1998. "Bargaining and market behavior in Jerusalem, Liubljana, Pittsburgh and Tokyo: an experimental study," Levine's Working Paper Archive 344, David K. Levine.
  22. Milgrom, Paul & Roberts, John, 1991. "Adaptive and sophisticated learning in normal form games," Games and Economic Behavior, Elsevier, vol. 3(1), pages 82-100, February.
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