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An effective replicator equation for games with a continuous strategy set

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  • Ruijgrok, Matthijs
  • Ruijgrok, Theo

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 Adaptive Dynamics.

Suggested Citation

  • Ruijgrok, Matthijs & Ruijgrok, Theo, 2013. "An effective replicator equation for games with a continuous strategy set," MPRA Paper 52198, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:52198
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    File URL: https://mpra.ub.uni-muenchen.de/52198/1/MPRA_paper_52198.pdf
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    References listed on IDEAS

    as
    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. Cressman, Ross, 2005. "Stability of the replicator equation with continuous strategy space," Mathematical Social Sciences, Elsevier, vol. 50(2), pages 127-147, September.
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    More about this item

    Keywords

    Evolutionary games; Replicator equation; Mutation; Dynamic stability; Partial differential equations;
    All these keywords.

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games

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