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On the Convergence of Fictitious Play

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  • Vijay Krishna
  • Tomas Sjostrom

Abstract

We study the continuous time Brown-Robinson fictitious play process f or non-zero sum games. We show that, in general, fictitious play cannot converg e cyclically to a mixed strategy equilibrium in which both players use more tha n two pure strategies.
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Suggested Citation

  • Vijay Krishna & Tomas Sjostrom, 1995. "On the Convergence of Fictitious Play," Harvard Institute of Economic Research Working Papers 1717, Harvard - Institute of Economic Research.
    • Handle: RePEc:fth:harver:1717
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    References listed on IDEAS

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    1. Monderer, Dov & Samet, Dov & Sela, Aner, 1997. "Belief Affirming in Learning Processes," Journal of Economic Theory, Elsevier, vol. 73(2), pages 438-452, April.
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    Cited by:

    1. JIMENEZ Edward, 2002. "Unified Game Theory," Computing in Economics and Finance 2002 25, Society for Computational Economics.
    2. Gale, Douglas & Rosenthal, Robert W., 1999. "Experimentation, Imitation, and Stochastic Stability," Journal of Economic Theory, Elsevier, vol. 84(1), pages 1-40, January.
    3. repec:hal:wpaper:hal-00713871 is not listed on IDEAS
    4. Berger, Ulrich, 2007. "Brown's original fictitious play," Journal of Economic Theory, Elsevier, vol. 135(1), pages 572-578, July.
    5. Harris, Christopher, 1998. "On the Rate of Convergence of Continuous-Time Fictitious Play," Games and Economic Behavior, Elsevier, vol. 22(2), pages 238-259, February.
    6. Ulrich Berger, 2003. "Continuous Fictitious Play via Projective Geometry," Game Theory and Information 0303004, University Library of Munich, Germany.
    7. Ulrich Berger, 2003. "Fictitious play in 2xn games," Game Theory and Information 0303009, University Library of Munich, Germany.
    8. Monderer, Dov & Samet, Dov & Sela, Aner, 1997. "Belief Affirming in Learning Processes," Journal of Economic Theory, Elsevier, vol. 73(2), pages 438-452, April.
    9. Monderer, Dov & Sela, Aner, 1997. "Fictitious play and- no-cycling conditions," Sonderforschungsbereich 504 Publications 97-12, Sonderforschungsbereich 504, Universität Mannheim;Sonderforschungsbereich 504, University of Mannheim.
    10. Alexander Zimper & Alexander Ludwig, 2007. "Attitude polarization," MEA discussion paper series 07155, Munich Center for the Economics of Aging (MEA) at the Max Planck Institute for Social Law and Social Policy.
    11. Ulrich Berger, 2003. "A general model of best response adaptation," Game Theory and Information 0303008, University Library of Munich, Germany.
    12. Ulrich Berger, 2004. "Two More Classes of Games with the Fictitious Play Property," Game Theory and Information 0408003, University Library of Munich, Germany.
    13. Alexander Zimper & Alexander Ludwig, 2009. "On attitude polarization under Bayesian learning with non-additive beliefs," Journal of Risk and Uncertainty, Springer, vol. 39(2), pages 181-212, October.
    14. Ellison, Glenn, 1997. "Learning from Personal Experience: One Rational Guy and the Justification of Myopia," Games and Economic Behavior, Elsevier, vol. 19(2), pages 180-210, May.

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    More about this item

    JEL classification:

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

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