Rational Learning Leads to Nash Equilibrium
AbstractEach of n players, in an infinitely repeated game, starts with subjective beliefs about his opponents' strategies. If the individual beliefs are compatible with the true strategies chose, then Bayesian updating will lead in the long run to accurate prediction of the future of play of the game. It follows that individual players, who know their own payoff matrices and choose strategies to maximize their expected utility, must eventually play according to a Nash equilibrium of the repeated game. 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.
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Bibliographic InfoPaper provided by Northwestern University, Center for Mathematical Studies in Economics and Management Science in its series Discussion Papers with number 925.
Date of creation: Mar 1990
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Other versions of this item:
- Kalai, Ehud & Lehrer, Ehud, 1991. "Rational Learning Leads to Nash Equilibrium," Working Papers 91-18, C.V. Starr Center for Applied Economics, New York University.
- Ehud Kalai & Ehud Lehrer, 1990. "Rational Learning Leads to Nash Equilibrium," Discussion Papers 895, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
- E. Kalai & E. Lehrer, 2010. "Rational Learning Leads to Nash Equilibrium," Levine's Working Paper Archive 529, David K. Levine.
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.:
- Aumann, Robert J. & Heifetz, Aviad, 2001.
1124, California Institute of Technology, Division of the Humanities and Social Sciences.
- 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.
- Mertens, J.-F., 1986. "Repeated games," CORE Discussion Papers 1986024, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
- V. Prasnikar & A. Roth, 1998.
"Considerations of fairness and strategy: experimental data from sequential games,"
Levine's Working Paper Archive
451, David K. Levine.
- 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.
- Jordan, J. S., 1985. "Learning rational expectations: The finite state case," Journal of Economic Theory, Elsevier, vol. 36(2), pages 257-276, August.
- Canning, David, 1992.
"Average behavior in learning models,"
Journal of Economic Theory,
Elsevier, vol. 57(2), pages 442-472, August.
- 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.
- Fudenberg, D. & Levine, D.K., 1991.
"Self-Confirming Equilibrium ,"
581, Massachusetts Institute of Technology (MIT), Department of Economics.
- Jordan, J. S., 1991. "Bayesian learning in normal form games," Games and Economic Behavior, Elsevier, vol. 3(1), pages 60-81, February.
- 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.
- 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.
- 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.
- Woodford, Michael, 1986.
"Learning to Believe in Sunspots,"
86-16, C.V. Starr Center for Applied Economics, New York University.
- Nyarko, Yaw, 1990.
"Learning In Mis-Specified Models And The Possibility Of Cycles,"
90-03, C.V. Starr Center for Applied Economics, New York University.
- 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.
- 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.
- Ehud Kalai & Ehud Lehrer, 1992.
"Weak and Strong Merging of Opinions,"
983, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
- Grandmont Jean-michel & Laroque G, 1990. "Economic dynamics with learning : some instability examples," CEPREMAP Working Papers (Couverture Orange) 9007, CEPREMAP.
- 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.
- Drew Fudenberg & David K. Levine, 1993.
"Steady State Learning and Nash Equilibrium,"
Levine's Working Paper Archive
373, David K. Levine.
- Ehud Kalai & Ehud Lehrer, 1991.
"Subjective Equilibrium in Repeated Games,"
981, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
- Monderer Dov & Samet Dov, 1995. "Stochastic Common Learning," Games and Economic Behavior, Elsevier, vol. 9(2), pages 161-171, May.
- Pearce, David G, 1984. "Rationalizable Strategic Behavior and the Problem of Perfection," Econometrica, Econometric Society, vol. 52(4), pages 1029-50, July.
- Rothschild, Michael, 1974. "A two-armed bandit theory of market pricing," Journal of Economic Theory, Elsevier, vol. 9(2), pages 185-202, October.
- Lawrence Blume & David Easley, 1993. "Rational Expectations and Rational Learning," Game Theory and Information 9307003, EconWPA.
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