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Continuous Approximations of Stochastic Evolutionary Game Dynamics

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  • Valentina Corradi
  • Rajiv Sarin

Abstract

We derive continuous approximations of stochastic evolutionary dynamics in games. Depending on how we construct the continuous limit, we obtain a continuous approxi-mation that is either an ordinary differential equation (ODE) or a stochastic differential equation (SDE). Our SDE approximation result provides the first derivation of a SDE from an underlying discrete stochastic evolutionary game model. In deriving both an ODE and a SDE limit from the same model, our results provide information regarding the conditions under which the different limits arise.

Suggested Citation

  • Valentina Corradi & Rajiv Sarin, "undated". "Continuous Approximations of Stochastic Evolutionary Game Dynamics," ELSE working papers 002, ESRC Centre on Economics Learning and Social Evolution.
  • Handle: RePEc:els:esrcls:002
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    References listed on IDEAS

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    1. Fudenberg, D. & Harris, C., 1992. "Evolutionary dynamics with aggregate shocks," Journal of Economic Theory, Elsevier, vol. 57(2), pages 420-441, August.
    2. Newey, Whitney K, 1991. "Uniform Convergence in Probability and Stochastic Equicontinuity," Econometrica, Econometric Society, vol. 59(4), pages 1161-1167, July.
    3. Jorgen W. Weibull, 1997. "Evolutionary Game Theory," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262731215, January.
    4. Borgers, Tilman & Sarin, Rajiv, 1997. "Learning Through Reinforcement and Replicator Dynamics," Journal of Economic Theory, Elsevier, vol. 77(1), pages 1-14, November.
    5. 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.
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    Cited by:

    1. Weibull, Jörgen W., 1997. "What have we learned from Evolutionary Game Theory so far?," Working Paper Series 487, Research Institute of Industrial Economics, revised 26 Oct 1998.
    2. Suren Basov, 2002. "Evolution of Social Behavior in the Global Economy: The Replicator Dynamics with Migration," Department of Economics - Working Papers Series 847, The University of Melbourne.
    3. Basov, S., 2001. "An Evolutionary Model of Reciprocity," Department of Economics - Working Papers Series 812, The University of Melbourne.
    4. Sandholm,W.H., 1999. "Markov evolution with inexact information," Working papers 15, Wisconsin Madison - Social Systems.
    5. Julide Yazar, 2006. "Evolving densities in continuous strategy games through particle simulations," Journal of Economic Interaction and Coordination, Springer;Society for Economic Science with Heterogeneous Interacting Agents, vol. 1(2), pages 171-187, November.
    6. Dawid, Herbert, 2007. "Evolutionary game dynamics and the analysis of agent-based imitation models: The long run, the medium run and the importance of global analysis," Journal of Economic Dynamics and Control, Elsevier, vol. 31(6), pages 2108-2133, June.

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