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A Result for Approximation of Imitational Behavior in Large Populations

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  • TANABE Yasuo

Abstract

This paper rigorously justifies the approximation of aggregate imitational behavior in large populations by the deterministic dynamics given by Bjonerstedt and Weibull. We first clarify what models fit their formulation, in which the stochastic dynamics depends only on the average frequencies of strategies in populations. Then we show that the stochastic process of each individual's behavior converges to a common McKean process and the average frequencies come to represent the deterministic dynamics of Bjonerstedt and Weibull when the number of individuals goes to infinity. Another derivation of replicator dynamics is also given by application to specific models of imitational behavior.

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  • TANABE Yasuo, 2004. "A Result for Approximation of Imitational Behavior in Large Populations," ESRI Discussion paper series 084, Economic and Social Research Institute (ESRI).
    • Handle: RePEc:esj:esridp:084
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    File URL: http://www.esri.go.jp/jp/archive/e_dis/e_dis090/e_dis084a.pdf
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    1. Borgers, Tilman & Sarin, Rajiv, 2000. "Naive Reinforcement Learning with Endogenous Aspirations," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 41(4), pages 921-950, November.
    2. Borgers, Tilman & Sarin, Rajiv, 1997. "Learning Through Reinforcement and Replicator Dynamics," Journal of Economic Theory, Elsevier, vol. 77(1), pages 1-14, November.
    3. 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.
    4. Dixon, Huw David, 2000. "Keeping up with the Joneses: competition and the evolution of collusion," Journal of Economic Behavior & Organization, Elsevier, vol. 43(2), pages 223-238, October.
    5. Jonas Bjoernerstedt & Karl H. Schlag, "undated". "On the Evolution of Imitative Behavior," ELSE working papers 029, ESRC Centre on Economics Learning and Social Evolution.
    6. Cabrales, Antonio, 2000. "Stochastic Replicator Dynamics," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 41(2), pages 451-481, May.
    7. Gale, John & Binmore, Kenneth G. & Samuelson, Larry, 1995. "Learning to be imperfect: The ultimatum game," Games and Economic Behavior, Elsevier, vol. 8(1), pages 56-90.
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