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Stability of the Replicator Equation for a Single-Species with a Multi-Dimensional Continuous Trait Space

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  • Cressman, Ross
  • Hofbauer, Josef
  • Riedel, Frank

Abstract

The replicator equation model for the evolution of individual behaviors in a single-species with a multi-dimensional continuous trait space is developed as a dynamics on the set of probability measures. Stability of monomorphisms in this model using the weak topology is compared to more traditional methods of adaptive dynamics. For quadratic fitness functions and initial normal trait distributions, it is shown that the multi-dimensional CSS (Continuously Stable Strategy) of adaptive dynamics is often relevant for predicting stability of the measure-theoretic model but may be too strong in general. For general fitness functions and trait distributions, the CSS is related to dominance solvability which can be used to characterize local stability for a large class of trait distributions that have no gaps in their supports whereas the stronger NIS (Neighborhood Invader Strategy) concept is needed if the supports are arbitrary.

Suggested Citation

  • Cressman, Ross & Hofbauer, Josef & Riedel, Frank, 2005. "Stability of the Replicator Equation for a Single-Species with a Multi-Dimensional Continuous Trait Space," Bonn Econ Discussion Papers 12/2005, University of Bonn, Bonn Graduate School of Economics (BGSE).
    • Handle: RePEc:zbw:bonedp:122005
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    File URL: https://www.econstor.eu/bitstream/10419/22918/1/bgse12_2005.pdf
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    References listed on IDEAS

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    Cited by:

    1. Hofbauer, Josef & Oechssler, Jörg & Riedel, Frank, 2009. "Brown-von Neumann-Nash dynamics: The continuous strategy case," Games and Economic Behavior, Elsevier, vol. 65(2), pages 406-429, March.
    2. repec:awi:wpaper:0424 is not listed on IDEAS

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