IDEAS home Printed from https://ideas.repec.org/p/cla/levarc/417.html
   My bibliography  Save this paper

On the Convergence of Fictitious Play

Author

Listed:
  • Vijay Krishna
  • T. Sjostrom

Abstract

We study the Brown-Robinson fictitious play process for non-zero sum games. We show that, in general, fictitious play cannot converge cyclically to a mixed strategy equilibrium in which both players use more than two pure strategies.
(This abstract was borrowed from another version of this item.)

Suggested Citation

  • Vijay Krishna & T. Sjostrom, 2010. "On the Convergence of Fictitious Play," Levine's Working Paper Archive 417, David K. Levine.
  • Handle: RePEc:cla:levarc:417
    as

    Download full text from publisher

    File URL: http://www.dklevine.com/archive/refs4417.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Fudenberg Drew & Kreps David M., 1993. "Learning Mixed Equilibria," Games and Economic Behavior, Elsevier, vol. 5(3), pages 320-367, July.
    2. Rubinstein, Ariel, 1991. "Comments on the Interpretation of Game Theory," Econometrica, Econometric Society, vol. 59(4), pages 909-924, July.
    3. Metrick, Andrew & Polak, Ben, 1994. "Fictitious Play in 2 x 2 Games: A Geometric Proof of Convergence," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 4(6), pages 923-933, October.
    4. Monderer, Dov & Samet, Dov & Sela, Aner, 1997. "Belief Affirming in Learning Processes," Journal of Economic Theory, Elsevier, vol. 73(2), pages 438-452, April.
    5. Crawford, Vincent P., 1985. "Learning behavior and mixed-strategy Nash equilibria," Journal of Economic Behavior & Organization, Elsevier, vol. 6(1), pages 69-78, March.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Ewerhart, Christian & Valkanova, Kremena, 2020. "Fictitious play in networks," Games and Economic Behavior, Elsevier, vol. 123(C), pages 182-206.
    2. Ulrich Berger, 2004. "Two More Classes of Games with the Fictitious Play Property," Game Theory and Information 0408003, University Library of Munich, Germany.
    3. Sela, Aner, 2000. "Fictitious Play in 2 x 3 Games," Games and Economic Behavior, Elsevier, vol. 31(1), pages 152-162, April.
    4. Hopkins, Ed, 1999. "Learning, Matching, and Aggregation," Games and Economic Behavior, Elsevier, vol. 26(1), pages 79-110, January.
    5. Oechssler, Jorg, 1997. "An Evolutionary Interpretation of Mixed-Strategy Equilibria," Games and Economic Behavior, Elsevier, vol. 21(1-2), pages 203-237, October.
    6. Benaim, Michel & Hirsch, Morris W., 1999. "Mixed Equilibria and Dynamical Systems Arising from Fictitious Play in Perturbed Games," Games and Economic Behavior, Elsevier, vol. 29(1-2), pages 36-72, October.
    7. Fudenberg, Drew & Levine, David K., 1995. "Consistency and cautious fictitious play," Journal of Economic Dynamics and Control, Elsevier, vol. 19(5-7), pages 1065-1089.
    8. Fudenberg, Drew & Levine, David, 1998. "Learning in games," European Economic Review, Elsevier, vol. 42(3-5), pages 631-639, May.
    9. Hoffmann, Eric, 2016. "On the learning and stability of mixed strategy Nash equilibria in games of strategic substitutes," Journal of Economic Behavior & Organization, Elsevier, vol. 130(C), pages 349-362.
    10. Echenique, Federico & Edlin, Aaron, 2004. "Mixed equilibria are unstable in games of strategic complements," Journal of Economic Theory, Elsevier, vol. 118(1), pages 61-79, September.
    11. Demichelis, Stefano & Germano, Fabrizio, 2002. "On (un)knots and dynamics in games," Games and Economic Behavior, Elsevier, vol. 41(1), pages 46-60, October.
    12. Berger, Ulrich, 2008. "Learning in games with strategic complementarities revisited," Journal of Economic Theory, Elsevier, vol. 143(1), pages 292-301, November.
    13. Rapoport, Amnon & Erev, Ido & Abraham, Elizabeth V. & Olson, David E., 1997. "Randomization and Adaptive Learning in a Simplified Poker Game," Organizational Behavior and Human Decision Processes, Elsevier, vol. 69(1), pages 31-49, January.
    14. Cox, James C. & Shachat, Jason & Walker, Mark, 2001. "An Experiment to Evaluate Bayesian Learning of Nash Equilibrium Play," Games and Economic Behavior, Elsevier, vol. 34(1), pages 11-33, January.
    15. Friedman, Daniel & Zhao, Shuchen, 2021. "When are mixed equilibria relevant?," Journal of Economic Behavior & Organization, Elsevier, vol. 191(C), pages 51-65.
    16. Gorodeisky, Ziv, 2009. "Deterministic approximation of best-response dynamics for the Matching Pennies game," Games and Economic Behavior, Elsevier, vol. 66(1), pages 191-201, May.
    17. Andrés Perea & Elias Tsakas, 2019. "Limited focus in dynamic games," International Journal of Game Theory, Springer;Game Theory Society, vol. 48(2), pages 571-607, June.
    18. Fudenberg, Drew & Levine, David K., 1999. "Conditional Universal Consistency," Games and Economic Behavior, Elsevier, vol. 29(1-2), pages 104-130, October.
    19. Mathieu Faure & Gregory Roth, 2010. "Stochastic Approximations of Set-Valued Dynamical Systems: Convergence with Positive Probability to an Attractor," Mathematics of Operations Research, INFORMS, vol. 35(3), pages 624-640, August.
    20. Anthonisen, Niels, 1997. "On the Convergence of Beliefs within Populations in Games with Learning," Journal of Economic Theory, Elsevier, vol. 76(1), pages 169-184, September.

    More about this item

    JEL classification:

    • C7 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory
    • D8 - Microeconomics - - Information, Knowledge, and Uncertainty

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:cla:levarc:417. 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: . General contact details of provider: http://www.dklevine.com/ .

    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 CitEc recognized a bibliographic reference but did not link an item in RePEc 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 RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: David K. Levine (email available below). General contact details of provider: http://www.dklevine.com/ .

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

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.