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Rational Learning Leads to Nash Equilibrium

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Author Info
Kalai, Ehud
Lehrer, Ehud

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Abstract

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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Publisher Info
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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References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
  1. Roth, Alvin E. & Vesna Prasnikar & Masahiro Okuno-Fujiwara & Shmuel Zamir, 1991. "Bargaining and Market Behavior in Jerusalem, Ljubljana, Pittsburgh, and Tokyo: An Experimental Study," American Economic Review, American Economic Association, vol. 81(5), pages 1068-95, December. [Downloadable!] (restricted)
  2. Ehud Kalai & Ehud Lehrer, 1991. "Private-Beliefs Equilibrium," Discussion Papers 926, Northwestern University, Center for Mathematical Studies in Economics and Management Science. [Downloadable!]
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  3. Woodford, Michael, 1990. "Learning to Believe in Sunspots," Econometrica, Econometric Society, vol. 58(2), pages 277-307, March. [Downloadable!] (restricted)
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  4. 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. [Downloadable!] (restricted)
  5. Fudenberg, Drew & Levine, David K, 1993. "Self-Confirming Equilibrium," Econometrica, Econometric Society, vol. 61(3), pages 523-45, May. [Downloadable!] (restricted)
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  6. Drew Fudenberg & David K. Levine, 1993. "Steady State Learning and Nash Equilibrium," Levine's Working Paper Archive 373, David K. Levine. [Downloadable!]
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  7. 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.
  8. Ehud Kalai & Ehud Lehrer, 1990. "Merging Economic Forecasts," Discussion Papers 1035, Northwestern University, Center for Mathematical Studies in Economics and Management Science. [Downloadable!]
  9. Grandmont Jean-michel & Laroque G, 1990. "Economic dynamics with learning : some instability examples," CEPREMAP Working Papers (Couverture Orange) 9007, CEPREMAP.
  10. 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. [Downloadable!] (restricted)
  11. 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. [Downloadable!] (restricted)
  12. Aumann, Robert J. & Heifetz, Aviad, 2002. "Incomplete information," Handbook of Game Theory with Economic Applications, in: R.J. Aumann & S. Hart (ed.), Handbook of Game Theory with Economic Applications, edition 1, volume 3, chapter 43, pages 1665-1686 Elsevier. [Downloadable!] (restricted)
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    • Aumann, Robert J. & Heifetz, Aviad, 2001. "Incomplete Information," Working Papers 1124, California Institute of Technology, Division of the Humanities and Social Sciences. [Downloadable!]
  13. Prasnikar, Vesna & Roth, Alvin E, 1992. "Considerations of Fairness and Strategy: Experimental Data from Sequential Games," The Quarterly Journal of Economics, MIT Press, vol. 107(3), pages 865-88, August. [Downloadable!] (restricted)
  14. Rothschild, Michael, 1974. "A two-armed bandit theory of market pricing," Journal of Economic Theory, Elsevier, vol. 9(2), pages 185-202, October. [Downloadable!] (restricted)
  15. Pearce, David G, 1984. "Rationalizable Strategic Behavior and the Problem of Perfection," Econometrica, Econometric Society, vol. 52(4), pages 1029-50, July. [Downloadable!] (restricted)
  16. Ehud Kalai & Ehud Lehrer, 1991. "Subjective Equilibrium in Repeated Games," Discussion Papers 981, Northwestern University, Center for Mathematical Studies in Economics and Management Science. [Downloadable!]
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  17. Canning, David, 1992. "Average behavior in learning models," Journal of Economic Theory, Elsevier, vol. 57(2), pages 442-472, August. [Downloadable!] (restricted)
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  18. Jordan, J. S., 1991. "Bayesian learning in normal form games," Games and Economic Behavior, Elsevier, vol. 3(1), pages 60-81, February. [Downloadable!] (restricted)
  19. Jordan, J. S., 1985. "Learning rational expectations: The finite state case," Journal of Economic Theory, Elsevier, vol. 36(2), pages 257-276, August. [Downloadable!] (restricted)
  20. Mertens, J.-F., 1986. "Repeated games," CORE Discussion Papers 1986024, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  21. Nyarko, Yaw, 1991. "Learning in mis-specified models and the possibility of cycles," Journal of Economic Theory, Elsevier, vol. 55(2), pages 416-427, December. [Downloadable!] (restricted)
  22. Linhart, Peter & Radner, Roy & Schotter, Andrew, 1990. "Behavior And Efficiency In The Sealed-Bid Mechanism," Working Papers 90-51, C.V. Starr Center for Applied Economics, New York University. [Downloadable!]
  23. Ehud Kalai & Ehud Lehrer, 1992. "Weak and Strong Merging of Opinions," Discussion Papers 983, Northwestern University, Center for Mathematical Studies in Economics and Management Science. [Downloadable!]
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