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Brown's Original Fictitious Play

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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

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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. Jiaxi Liu & Shuyi Lin & Linwei Xin & Yidong Zhang, 2023. "AI vs. Human Buyers: A Study of Alibaba’s Inventory Replenishment System," Interfaces, INFORMS, vol. 53(5), pages 372-387, September.
    3. Vinil T Chackochan & Vittorio Sanguineti, 2019. "Incomplete information about the partner affects the development of collaborative strategies in joint action," PLOS Computational Biology, Public Library of Science, vol. 15(12), pages 1-23, December.
    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.
    6. Dimitris Batzilis & Sonia Jaffe & Steven Levitt & John A. List & Jeffrey Picel, 2019. "Behavior in Strategic Settings: Evidence from a Million Rock-Paper-Scissors Games," Games, MDPI, vol. 10(2), pages 1-34, April.
    7. Zhao, Huan, 2011. "Four Market Studies for the Beef and Electric Power Industries," ISU General Staff Papers 201101010800001360, Iowa State University, Department of Economics.
    8. 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.
    9. Stefan Rass & Sandra König & Stefan Schauer, 2017. "Defending Against Advanced Persistent Threats Using Game-Theory," PLOS ONE, Public Library of Science, vol. 12(1), pages 1-43, January.

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    More about this item

    Keywords

    Fictitious Play; Learning Process; Ordinal Potential Games;
    All these keywords.

    JEL classification:

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

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