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Brown's Original Fictitious Play

Author

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  • Ulrich Berger

    (Vienna Univrsity of Economics)

Abstract

What modern game theorists describe as 'fictitious play' is not the learning process George W. Brown defined in his 1951 paper. His original version differs in a subtle detail, namely the order of belief updating. In this note we revive Brown's original fictitious play process and demonstrate that this seemingly innocent detail allows for an extremely simple and intuitive proof of convergence in an interesting and large class of games: nondegenerate ordinal potential games.

Suggested Citation

  • Ulrich Berger, 2005. "Brown's Original Fictitious Play," Game Theory and Information 0503008, University Library of Munich, Germany.
  • Handle: RePEc:wpa:wuwpga:0503008
    Note: Type of Document - pdf; pages: 12
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    References listed on IDEAS

    as
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    5. Ross Cressman, 2003. "Evolutionary Dynamics and Extensive Form Games," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262033054, November.
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    7. Sela, Aner, 2000. "Fictitious Play in 2 x 3 Games," Games and Economic Behavior, Elsevier, vol. 31(1), pages 152-162, April.
    8. Monderer, Dov & Sela, Aner, 1996. "A2 x 2Game without the Fictitious Play Property," Games and Economic Behavior, Elsevier, vol. 14(1), pages 144-148, May.
    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. Hahn, Sunku, 1999. "The convergence of fictitious play in 3 x 3 games with strategic complementarities," Economics Letters, Elsevier, vol. 64(1), pages 57-60, July.
    11. Ulrich Berger, 2004. "Two More Classes of Games with the Fictitious Play Property," Game Theory and Information 0408003, University Library of Munich, Germany.
    12. Vijay Krishna & Tomas Sjöström, 1998. "On the Convergence of Fictitious Play," Mathematics of Operations Research, INFORMS, vol. 23(2), pages 479-511, May.
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    14. Foster, Dean P. & Young, H. Peyton, 1998. "On the Nonconvergence of Fictitious Play in Coordination Games," Games and Economic Behavior, Elsevier, vol. 25(1), pages 79-96, October.
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    Cited by:

    1. Ulrich Berger, 2012. "Non-algebraic Convergence Proofs for Continuous-Time Fictitious Play," Dynamic Games and Applications, Springer, vol. 2(1), pages 4-17, March.
    2. Zhao, Huan, 2011. "Four Market Studies for the Beef and Electric Power Industries," ISU General Staff Papers 201101010800001360, Iowa State University, Department of Economics.
    3. Berger, Ulrich, 2007. "Two more classes of games with the continuous-time fictitious play property," Games and Economic Behavior, Elsevier, vol. 60(2), pages 247-261, August.
    4. In, Younghwan, 2014. "Fictitious play property of the Nash demand game," Economics Letters, Elsevier, vol. 122(3), pages 408-412.
    5. Berger, Ulrich, 2008. "Learning in games with strategic complementarities revisited," Journal of Economic Theory, Elsevier, vol. 143(1), pages 292-301, November.

    More about this item

    Keywords

    Fictitious Play; Learning Process; Ordinal Potential Games;

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games

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