IDEAS home Printed from https://ideas.repec.org/
MyIDEAS: Login to save this paper or follow this series

Rational Learning Leads to Nash Equilibrium

  • Ehud Kalai
  • Ehud Lehrer

Each 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.

If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.

File URL: http://www.kellogg.northwestern.edu/research/math/papers/925.pdf
File Function: main text
Download Restriction: no

Paper provided by Northwestern University, Center for Mathematical Studies in Economics and Management Science in its series Discussion Papers with number 925.

as
in new window

Length:
Date of creation: Mar 1990
Date of revision:
Handle: RePEc:nwu:cmsems:925
Contact details of provider: Postal: Center for Mathematical Studies in Economics and Management Science, Northwestern University, 580 Jacobs Center, 2001 Sheridan Road, Evanston, IL 60208-2014
Phone: 847/491-3527
Fax: 847/491-2530
Web page: http://www.kellogg.northwestern.edu/research/math/
Email:


More information through EDIRC

Order Information: Email:


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.:

as in new window
  1. Jordan, J. S., 1991. "Bayesian learning in normal form games," Games and Economic Behavior, Elsevier, vol. 3(1), pages 60-81, February.
  2. 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.
  3. Lawrence Blume & David Easley, 1993. "Rational Expectations and Rational Learning," Game Theory and Information 9307003, EconWPA.
  4. Jordan, J. S., 1985. "Learning rational expectations: The finite state case," Journal of Economic Theory, Elsevier, vol. 36(2), pages 257-276, August.
  5. Fudenberg, Drew & Levine, David K, 1993. "Self-Confirming Equilibrium," Econometrica, Econometric Society, vol. 61(3), pages 523-45, May.
  6. D. Canning, 2010. "Average Behavior in Learning Models," Levine's Working Paper Archive 490, David K. Levine.
  7. Woodford, Michael, 1986. "Learning to Believe in Sunspots," Working Papers 86-16, C.V. Starr Center for Applied Economics, New York University.
  8. 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.
  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. Drew Fudenberg & David K. Levine, 1993. "Steady State Learning and Nash Equilibrium," Levine's Working Paper Archive 373, David K. Levine.
  11. Aumann, Robert J. & Heifetz, Aviad, 2001. "Incomplete Information," Working Papers 1124, California Institute of Technology, Division of the Humanities and Social Sciences.
  12. 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).
  13. Pearce, David G, 1984. "Rationalizable Strategic Behavior and the Problem of Perfection," Econometrica, Econometric Society, vol. 52(4), pages 1029-50, July.
  14. Ehud Kalai & Ehud Lehrer, 1991. "Subjective Equilibrium in Repeated Games," Discussion Papers 981, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  15. 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.
  16. V. Prasnikar & A. Roth, 1998. "Considerations of fairness and strategy: experimental data from sequential games," Levine's Working Paper Archive 451, David K. Levine.
  17. 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.
  18. Mertens, J.-F., 1986. "Repeated games," CORE Discussion Papers 1986024, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  19. 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.
  20. Grandmont Jean-michel & Laroque G, 1990. "Economic dynamics with learning : some instability examples," CEPREMAP Working Papers (Couverture Orange) 9007, CEPREMAP.
  21. Rothschild, Michael, 1974. "A two-armed bandit theory of market pricing," Journal of Economic Theory, Elsevier, vol. 9(2), pages 185-202, October.
  22. 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.
  23. Monderer Dov & Samet Dov, 1995. "Stochastic Common Learning," Games and Economic Behavior, Elsevier, vol. 9(2), pages 161-171, May.
Full references (including those not matched with items on IDEAS)

This item is not listed on Wikipedia, on a reading list or among the top items on IDEAS.

When requesting a correction, please mention this item's handle: RePEc:nwu:cmsems:925. 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 you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

If references are entirely missing, you can add them using this form.

If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.

If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.

Please note that corrections may take a couple of weeks to filter through the various RePEc services.

This information is provided to you by IDEAS at the Research Division of the Federal Reserve Bank of St. Louis using RePEc data.