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A general model of best response adaptation

Author

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  • Ulrich Berger

    (Vienna University of Economics)

Abstract

We develop a general model of best response adaptation in large populations for symmetric and asymmetric conflicts with role-switching. For special cases including the classical best response dynamics and the symmetrized best response dynamics we show that the set of Nash equilibria is attracting for zero-sum games. For asymmetric conflicts and equally large populations, convergence to a Nash equilibrium in the base game implies convergence to a Nash equilibrium on the Wright manifold in the role game.

Suggested Citation

  • Ulrich Berger, 2003. "A general model of best response adaptation," Game Theory and Information 0303008, University Library of Munich, Germany.
  • Handle: RePEc:wpa:wuwpga:0303008
    Note: Type of Document - pdf-file; pages: 21; figures: included
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    File URL: https://econwpa.ub.uni-muenchen.de/econ-wp/game/papers/0303/0303008.pdf
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    References listed on IDEAS

    as
    1. Samuelson, L., 1989. "Evolutionnary Stability In Asymmetric Games," Papers 11-8-2, Pennsylvania State - Department of Economics.
    2. Fudenberg, Drew & Levine, David, 1998. "Learning in games," European Economic Review, Elsevier, vol. 42(3-5), pages 631-639, May.
    3. Berger, Ulrich & Hofbauer, Josef, 2006. "Irrational behavior in the Brown-von Neumann-Nash dynamics," Games and Economic Behavior, Elsevier, vol. 56(1), pages 1-6, July.
    4. Cressman, R., 2000. "Subgame Monotonicity in Extensive Form Evolutionary Games," Games and Economic Behavior, Elsevier, vol. 32(2), pages 183-205, August.
    5. Borgers, Tilman & Sarin, Rajiv, 1997. "Learning Through Reinforcement and Replicator Dynamics," Journal of Economic Theory, Elsevier, vol. 77(1), pages 1-14, November.
    6. Gilboa, Itzhak & Matsui, Akihiko, 1991. "Social Stability and Equilibrium," Econometrica, Econometric Society, vol. 59(3), pages 859-867, May.
    7. 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.
    8. Ulrich Berger, 2002. "Best response dynamics for role games," International Journal of Game Theory, Springer;Game Theory Society, vol. 30(4), pages 527-538.
    9. Ulrich Berger, 2003. "Continuous Fictitious Play via Projective Geometry," Game Theory and Information 0303004, University Library of Munich, Germany.
    10. Schlag, Karl H., 1998. "Why Imitate, and If So, How?, : A Boundedly Rational Approach to Multi-armed Bandits," Journal of Economic Theory, Elsevier, vol. 78(1), pages 130-156, January.
    11. Friedman, Daniel, 1991. "Evolutionary Games in Economics," Econometrica, Econometric Society, vol. 59(3), pages 637-666, May.
    12. Vijay Krishna & Tomas Sjöström, 1998. "On the Convergence of Fictitious Play," Mathematics of Operations Research, INFORMS, vol. 23(2), pages 479-511, May.
    13. Binmore, Ken & Samuelson, Larry, 2001. "Evolution and Mixed Strategies," Games and Economic Behavior, Elsevier, vol. 34(2), pages 200-226, February.
    14. Nachbar, J H, 1990. ""Evolutionary" Selection Dynamics in Games: Convergence and Limit Properties," International Journal of Game Theory, Springer;Game Theory Society, vol. 19(1), pages 59-89.
    15. Matsui, Akihiko, 1992. "Best response dynamics and socially stable strategies," Journal of Economic Theory, Elsevier, vol. 57(2), pages 343-362, August.
    16. Monderer, Dov & Shapley, Lloyd S., 1996. "Potential Games," Games and Economic Behavior, Elsevier, vol. 14(1), pages 124-143, May.
    17. Ross Cressman & Andrea Gaunersdorfer & Jean-François Wen, 2000. "Evolutionary And Dynamic Stability In Symmetric Evolutionary Games With Two Independent Decisions," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 2(01), pages 67-81.
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    More about this item

    Keywords

    Role Games; Best Response Adaptation; Learning; Evolution;

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • D83 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Search; Learning; Information and Knowledge; Communication; Belief; Unawareness

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