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A Note on Best Response Dynamics

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  • Hopkins, Ed

Abstract

We investigate the relationship between the continuous time best response dynamic, its perturbed version and evolutionary dynamics in relation to mixed strategy equilibria. We find that as the level of noise approaches zero, the perturbed best response dynamic has the same quantitative properties as a broad class of evolutionary dynamics. That is, stability properties of equilibria are robust across learning dynamics of quite different origins and motivations.
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  • Hopkins, Ed, 1999. "A Note on Best Response Dynamics," Games and Economic Behavior, Elsevier, vol. 29(1-2), pages 138-150, October.
    • Handle: RePEc:eee:gamebe:v:29:y:1999:i:1-2:p:138-150
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    References listed on IDEAS

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    1. Fudenberg Drew & Kreps David M., 1993. "Learning Mixed Equilibria," Games and Economic Behavior, Elsevier, vol. 5(3), pages 320-367, July.
    2. Ed Hopkins, "undated". "Price Dispersion: An Evolutionary Approach," Department of Economics 1996 : III, Edinburgh School of Economics, University of Edinburgh.
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    8. Martin Posch, 1997. "Cycling in a stochastic learning algorithm for normal form games," Journal of Evolutionary Economics, Springer, vol. 7(2), pages 193-207.
    9. Borgers, Tilman & Sarin, Rajiv, 1997. "Learning Through Reinforcement and Replicator Dynamics," Journal of Economic Theory, Elsevier, vol. 77(1), pages 1-14, November.
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    11. Benaim, Michel & Hirsch, Morris W., 1999. "Mixed Equilibria and Dynamical Systems Arising from Fictitious Play in Perturbed Games," Games and Economic Behavior, Elsevier, vol. 29(1-2), pages 36-72, October.
    12. Cressman, R., 1997. "Local stability of smooth selection dynamics for normal form games," Mathematical Social Sciences, Elsevier, vol. 34(1), pages 1-19, August.
    13. 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.
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    More about this item

    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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