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An Effective Replicator Equation for Games with a Continuous Strategy Set

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  • M. Ruijgrok
  • Th. Ruijgrok

Abstract

The replicator equation for a two-person symmetric game, which has an interval of the real line as strategy space, is extended with a mutation term. Assuming that the distribution of the strategies has a continuous density, a partial differential equation for this density is derived. The equation is analysed for two examples. A connection is made with the canonical equation from adaptive dynamics and the continuous stable strategy criterion. Copyright Springer Science+Business Media New York 2015

Suggested Citation

  • M. Ruijgrok & Th. Ruijgrok, 2015. "An Effective Replicator Equation for Games with a Continuous Strategy Set," Dynamic Games and Applications, Springer, vol. 5(2), pages 157-179, June.
    • Handle: RePEc:spr:dyngam:v:5:y:2015:i:2:p:157-179
    DOI: 10.1007/s13235-014-0118-y
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    References listed on IDEAS

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    1. Oechssler, Jorg & Riedel, Frank, 2002. "On the Dynamic Foundation of Evolutionary Stability in Continuous Models," Journal of Economic Theory, Elsevier, vol. 107(2), pages 223-252, December.
    2. U. Dieckmann & R. Law, 1996. "The Dynamical Theory of Coevolution: A Derivation from Stochastic Ecological Processes," Working Papers wp96001, International Institute for Applied Systems Analysis.
    3. Hisashi Ohtsuki, 2011. "Evolutionary Dynamics of the Nash Demand Game: A Diffusion Approach," Dynamic Games and Applications, Springer, vol. 1(3), pages 449-461, September.
    4. Friedman, Daniel & Ostrov, Daniel N., 2013. "Evolutionary dynamics over continuous action spaces for population games that arise from symmetric two-player games," Journal of Economic Theory, Elsevier, vol. 148(2), pages 743-777.
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