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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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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
Contact details of provider: 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
Web page: http://econ.as.nyu.edu/object/econ.cvstarr.html
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  1. Fudenberg, D. & Levine, D.K., 1991. "Self-Confirming Equilibrium ," Working papers 581, Massachusetts Institute of Technology (MIT), Department of Economics.
  2. 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.
  3. 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.
  4. Vesna Prasnikar & Alvin E. Roth, 1992. "Considerations of Fairness and Strategy: Experimental Data from Sequential Games," The Quarterly Journal of Economics, Oxford University Press, vol. 107(3), pages 865-888.
  5. 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.
  6. Mertens,Jean-François & Sorin,Sylvain & Zamir,Shmuel, 2015. "Repeated Games," Cambridge Books, Cambridge University Press, number 9781107662636, June.
    • Mertens,Jean-François & Sorin,Sylvain & Zamir,Shmuel, 2015. "Repeated Games," Cambridge Books, Cambridge University Press, number 9781107030206, June.
  7. Jordan, J. S., 1991. "Bayesian learning in normal form games," Games and Economic Behavior, Elsevier, vol. 3(1), pages 60-81, February.
  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.
  9. repec:cor:louvrp:-636 is not listed on IDEAS
  10. 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.
  11. 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.
  12. Kalai, Ehud & Lehrer, Ehud, 1994. "Weak and strong merging of opinions," Journal of Mathematical Economics, Elsevier, vol. 23(1), pages 73-86, January.
  13. Fudenberg, Drew & Levine, David K, 1993. "Steady State Learning and Nash Equilibrium," Econometrica, Econometric Society, vol. 61(3), pages 547-73, May.
  14. Woodford, Michael, 1990. "Learning to Believe in Sunspots," Econometrica, Econometric Society, vol. 58(2), pages 277-307, March.
  15. Jordan, J. S., 1985. "Learning rational expectations: The finite state case," Journal of Economic Theory, Elsevier, vol. 36(2), pages 257-276, August.
  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. Pearce, David G, 1984. "Rationalizable Strategic Behavior and the Problem of Perfection," Econometrica, Econometric Society, vol. 52(4), pages 1029-50, July.
  19. Canning, David, 1992. "Average behavior in learning models," Journal of Economic Theory, Elsevier, vol. 57(2), pages 442-472, August.
  20. Lawrence Blume & David Easley, 1993. "Rational Expectations and Rational Learning," Game Theory and Information 9307003, EconWPA.
  21. 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.
  22. Monderer Dov & Samet Dov, 1995. "Stochastic Common Learning," Games and Economic Behavior, Elsevier, vol. 9(2), pages 161-171, May.
  23. Grandmont Jean-michel & Laroque G, 1990. "Economic dynamics with learning : some instability examples," CEPREMAP Working Papers (Couverture Orange) 9007, CEPREMAP.
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