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Rational Learning Leads to Nash Equilibrium

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  • Kalai, Ehud
  • Lehrer, Ehud

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.

(This abstract was borrowed from another version of this item.)

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File URL: http://econ.as.nyu.edu/docs/IO/9392/RR91-18.pdf
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Bibliographic Info

Paper provided by C.V. Starr Center for Applied Economics, New York University in its series Working Papers with number 91-18.

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Length: 34 pages
Date of creation: 1991
Date of revision:
Handle: RePEc:cvs:starer:91-18

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Postal: C.V. Starr Center, Department of Economics, New York University, 19 W. 4th Street, 6th Floor, New York, NY 10012
Phone: (212) 998-8936
Fax: (212) 995-3932
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Web page: http://econ.as.nyu.edu/object/econ.cvstarr.html
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Postal: C.V. Starr Center, Department of Economics, New York University, 19 W. 4th Street, 6th Floor, New York, NY 10012
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Related research

Keywords: Games ; strategies ; economic information ; time factor;

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References

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  1. 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.
  2. 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.
  3. Drew Fudenberg & David K. Levine, 1993. "Self-Confirming Equilibrium," Levine's Working Paper Archive 2147, David K. Levine.
  4. Monderer Dov & Samet Dov, 1995. "Stochastic Common Learning," Games and Economic Behavior, Elsevier, vol. 9(2), pages 161-171, May.
  5. Kalai, Ehud & Lehrer, Ehud, 1993. "Subjective Equilibrium in Repeated Games," Econometrica, Econometric Society, vol. 61(5), pages 1231-40, September.
  6. Woodford, Michael, 1990. "Learning to Believe in Sunspots," Econometrica, Econometric Society, vol. 58(2), pages 277-307, March.
  7. V. Prasnikar & A. Roth, 1998. "Considerations of fairness and strategy: experimental data from sequential games," Levine's Working Paper Archive 451, David K. Levine.
  8. Drew Fudenberg & David K. Levine, 1993. "Steady State Learning and Nash Equilibrium," Levine's Working Paper Archive 373, David K. Levine.
  9. 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.
  10. D. Canning, 2010. "Average Behavior in Learning Models," Levine's Working Paper Archive 490, David K. Levine.
  11. Pearce, David G, 1984. "Rationalizable Strategic Behavior and the Problem of Perfection," Econometrica, Econometric Society, vol. 52(4), pages 1029-50, July.
  12. Lawrence Blume & David Easley, 1993. "Rational Expectations and Rational Learning," Game Theory and Information 9307003, EconWPA.
  13. 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.
  14. Rothschild, Michael, 1974. "A two-armed bandit theory of market pricing," Journal of Economic Theory, Elsevier, vol. 9(2), pages 185-202, October.
  15. Grandmont Jean-michel & Laroque G, 1990. "Economic dynamics with learning : some instability examples," CEPREMAP Working Papers (Couverture Orange) 9007, CEPREMAP.
  16. 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.
  17. Mertens, J.-F., 1986. "Repeated games," CORE Discussion Papers 1986024, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  18. 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.
  19. 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.
  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. Aumann, Robert J. & Heifetz, Aviad, 2001. "Incomplete Information," Working Papers 1124, California Institute of Technology, Division of the Humanities and Social Sciences.
  22. HART, Sergiu, . "Nonzerosum two-person repeated games with incomplete information," CORE Discussion Papers RP -636, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  23. Jordan, J. S., 1991. "Bayesian learning in normal form games," Games and Economic Behavior, Elsevier, vol. 3(1), pages 60-81, February.
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