Rational Learning Leads to Nash Equilibrium
Two players are about to play a discounted infinitely repeated bimatrix game. Each player knows his own payoff matrix and chooses a strategy which is a best response to some private beliefs over strategies chosen by his opponent. If both players' beliefs contain a grain of truth (each assigns some positive probability to the strategy chosen by the opponent), then they will eventually (a) accurately predict the future play of the game and (b) play a Nash equilibrium of the repeated game. An immediate corollary is that in playing a Harsanyi-Nash equilibrium of a discounted repeated game of incomplete information about opponents' payoffs, the players will eventually play an equilibrium of the real game as if they had complete information.
|Date of creation:||Mar 1990|
|Date of revision:|
|Contact details of provider:|| Postal: |
Web page: http://www.kellogg.northwestern.edu/research/math/
More information through EDIRC
|Order Information:|| Email: |
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.:
- 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.
- Nyarko, Yaw, 1990. "Learning In Mis-Specified Models And The Possibility Of Cycles," Working Papers 90-03, C.V. Starr Center for Applied Economics, New York University.
- Aumann, Robert J. & Heifetz, Aviad, 2002.
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
- Monderer Dov & Samet Dov, 1995. "Stochastic Common Learning," Games and Economic Behavior, Elsevier, vol. 9(2), pages 161-171, May.
- 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.
- repec:cup:cbooks:9781107030206 is not listed on IDEAS
- Drew Fudenberg & David K. Levine, 1993.
"Steady State Learning and Nash Equilibrium,"
Levine's Working Paper Archive
373, David K. Levine.
- 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.
- Rothschild, Michael, 1974. "A two-armed bandit theory of market pricing," Journal of Economic Theory, Elsevier, vol. 9(2), pages 185-202, October.
- Jordan, J. S., 1991. "Bayesian learning in normal form games," Games and Economic Behavior, Elsevier, vol. 3(1), pages 60-81, February.
- Woodford, Michael, 1990.
"Learning to Believe in Sunspots,"
Econometric Society, vol. 58(2), pages 277-307, March.
- Lawrence Blume & David Easley, 1993. "Rational Expectations and Rational Learning," Game Theory and Information 9307003, EconWPA.
- 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.
- Fudenberg, D. & Levine, D.K., 1991.
"Self-Confirming Equilibrium ,"
581, Massachusetts Institute of Technology (MIT), Department of Economics.
- Grandmont Jean-michel & Laroque G, 1990. "Economic dynamics with learning : some instability examples," CEPREMAP Working Papers (Couverture Orange) 9007, CEPREMAP.
- Mertens, J.-F., 1986.
CORE Discussion Papers
1986024, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
- Ehud Kalai & Ehud Lehrer, 1992.
"Weak and Strong Merging of Opinions,"
983, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
- Kalai, Ehud & Lehrer, Ehud, 1993.
"Subjective Equilibrium in Repeated Games,"
Econometric Society, vol. 61(5), pages 1231-40, September.
- Pearce, David G, 1984. "Rationalizable Strategic Behavior and the Problem of Perfection," Econometrica, Econometric Society, vol. 52(4), pages 1029-50, July.
- 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.
- Jordan, J. S., 1985. "Learning rational expectations: The finite state case," Journal of Economic Theory, Elsevier, vol. 36(2), pages 257-276, August.
- Canning, D., 1990.
"Average Behaviour In Learning Models,"
156, Cambridge - Risk, Information & Quantity Signals.
- 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.
- 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.
- repec:cor:louvrp:-636 is not listed on IDEAS
When requesting a correction, please mention this item's handle: RePEc:nwu:cmsems:895. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Fran Walker)
If references are entirely missing, you can add them using this form.