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Brown's original fictitious play

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  • Berger, Ulrich

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.
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  • Berger, Ulrich, 2007. "Brown's original fictitious play," Journal of Economic Theory, Elsevier, vol. 135(1), pages 572-578, July.
    • Handle: RePEc:eee:jetheo:v:135:y:2007:i:1:p:572-578
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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.
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    3. Zhao, Huan, 2011. "Four Market Studies for the Beef and Electric Power Industries," ISU General Staff Papers 201101010800001360, Iowa State University, Department of Economics.
    4. 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.
    5. 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.
    6. In, Younghwan, 2014. "Fictitious play property of the Nash demand game," Economics Letters, Elsevier, vol. 122(3), pages 408-412.
    7. Berger, Ulrich, 2008. "Learning in games with strategic complementarities revisited," Journal of Economic Theory, Elsevier, vol. 143(1), pages 292-301, November.
    8. 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.
    9. 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.

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    JEL classification:

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

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