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A Generalized Model Of Best Response Adaptation

Author

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  • ULRICH BERGER

    (Department of Economics, VW 5, Vienna University of Economics and Business, Administration, Augasse 2-6, A-1090 Vienna, Austria)

Abstract

We present a generalized model of myopic best response adaptation in large populations. In asymmetric conflicts, individuals can be in the role of the row player or the column player. The idea that an individual's role need not be fixed is introduced explicitly in our model by a process of role switching. The best response dynamics, the symmetrized best response dynamics, and the continuous time fictitious play process are included as special cases. We show that the set of Nash equilibria is attracting for zero-sum games. Moreover, for any base game, convergence to a Nash equilibrium implies convergence to a Nash equilibrium on the Wright manifold in the role game.

Suggested Citation

  • Ulrich Berger, 2006. "A Generalized Model Of Best Response Adaptation," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 8(01), pages 45-66.
    • Handle: RePEc:wsi:igtrxx:v:08:y:2006:i:01:n:s0219198906000783
    DOI: 10.1142/S0219198906000783
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    References listed on IDEAS

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    1. Fudenberg, Drew & Levine, David, 1998. "Learning in games," European Economic Review, Elsevier, vol. 42(3-5), pages 631-639, May.
    2. ., 1998. "Economic History," Chapters, in: John B. Davis & D. W. Hands & Uskali Mäki (ed.), The Handbook of Economic Methodology, chapter 27, Edward Elgar Publishing.
    3. Ross Cressman, 2003. "Evolutionary Dynamics and Extensive Form Games," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262033054, April.
    4. Drew Fudenberg & David K. Levine, 1998. "The Theory of Learning in Games," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262061945, April.
    5. Ulrich Berger, 2004. "Two More Classes of Games with the Fictitious Play Property," Game Theory and Information 0408003, University Library of Munich, Germany.
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    Cited by:

    1. Ewerhart, Christian & Valkanova, Kremena, 2020. "Fictitious play in networks," Games and Economic Behavior, Elsevier, vol. 123(C), pages 182-206.
    2. Sawa, Ryoji & Zusai, Dai, 2014. "Evolutionary imitative dynamics with population-varying aspiration levels," Journal of Economic Theory, Elsevier, vol. 154(C), pages 562-577.

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    More about this item

    Keywords

    Role games; best reply dynamics; best response dynamics; fictitious play; Journal of Economic Literature Classification Numbers: C72; Journal of Economic Literature Classification Numbers: D83;
    All these keywords.

    JEL classification:

    • B4 - Schools of Economic Thought and Methodology - - Economic Methodology
    • C0 - Mathematical and Quantitative Methods - - General
    • C6 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling
    • C7 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory
    • D5 - Microeconomics - - General Equilibrium and Disequilibrium
    • D7 - Microeconomics - - Analysis of Collective Decision-Making
    • M2 - Business Administration and Business Economics; Marketing; Accounting; Personnel Economics - - Business Economics

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