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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. Newey, Whitney K, 1991. "Uniform Convergence in Probability and Stochastic Equicontinuity," Econometrica, Econometric Society, vol. 59(4), pages 1161-1167, July.
    2. Jorgen W. Weibull, 1997. "Evolutionary Game Theory," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262731215, April.
    3. Borgers, Tilman & Sarin, Rajiv, 1997. "Learning Through Reinforcement and Replicator Dynamics," Journal of Economic Theory, Elsevier, vol. 77(1), pages 1-14, November.
    4. Fudenberg, D. & Harris, C., 1992. "Evolutionary dynamics with aggregate shocks," Journal of Economic Theory, Elsevier, vol. 57(2), pages 420-441, August.
    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. Ianni, A., 2002. "Reinforcement learning and the power law of practice: some analytical results," Discussion Paper Series In Economics And Econometrics 203, Economics Division, School of Social Sciences, University of Southampton.
    3. 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.
    4. Dai, Darong & Shen, Kunrong, 2012. "A New Stationary Game Equilibrium Induced by Stochastic Group Evolution and Rational Individual Choice," MPRA Paper 40586, University Library of Munich, Germany, revised 09 Aug 2012.
    5. Basov, S., 2001. "An Evolutionary Model of Reciprocity," Department of Economics - Working Papers Series 812, The University of Melbourne.
    6. Sandholm,W.H., 1999. "Markov evolution with inexact information," Working papers 15, Wisconsin Madison - Social Systems.
    7. Konstantin Avrachenkov & Vivek S. Borkar, 2019. "Metastability in Stochastic Replicator Dynamics," Dynamic Games and Applications, Springer, vol. 9(2), pages 366-390, June.
    8. Tanabe, Yasuo, 2006. "The propagation of chaos for interacting individuals in a large population," Mathematical Social Sciences, Elsevier, vol. 51(2), pages 125-152, March.
    9. Alanyali, Murat, 2010. "A note on adjusted replicator dynamics in iterated games," Journal of Mathematical Economics, Elsevier, vol. 46(1), pages 86-98, January.
    10. Vassili Kolokoltsov, 2017. "The Evolutionary Game of Pressure (or Interference), Resistance and Collaboration," Mathematics of Operations Research, INFORMS, vol. 42(4), pages 915-944, November.
    11. 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.
    12. Sandholm, William H., 2003. "Evolution and equilibrium under inexact information," Games and Economic Behavior, Elsevier, vol. 44(2), pages 343-378, August.
    13. 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.
    14. Dai, Darong & Shen, Kunrong, 2012. "A new stationary game equilibrium induced by stochastic group evolution and rational Individual choice," MPRA Paper 40133, University Library of Munich, Germany.

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