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On the Evolutionary Selection of Nash Equilibrium Components

Author

Listed:
  • Dieter Balkenborg

    (Department of Economics, University of Exeter)

  • Karl H. Schlag

    (Department of Economics, European University Institute)

Abstract

It is well known for the common multi-population evolutionary dynamics applied to normal form games that a pure strategy combination is asymptotically stable if and only if it is a strict equilibrium point. We extend this result to sets as follows. For certain regular selection dynamics every connected and closed asymptotically stable set of rest points containing a pure strategy combination is a strict equilibrium set and hence a Nash equilibrium component. A converse statement holds for two person games, for convex strict equilibrium sets and for the standard replicator dynamic.

Suggested Citation

  • Dieter Balkenborg & Karl H. Schlag, 2001. "On the Evolutionary Selection of Nash Equilibrium Components," Discussion Papers 0106, University of Exeter, Department of Economics.
    • Handle: RePEc:exe:wpaper:0106
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    File URL: https://exetereconomics.github.io/RePEc/dpapers/DP0106.pdf
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    Cited by:

    1. Demichelis, Stefano & Ritzberger, Klaus, 2003. "From evolutionary to strategic stability," Journal of Economic Theory, Elsevier, vol. 113(1), pages 51-75, November.

    More about this item

    Keywords

    evolutionary dynamics; replicator dynamic; regular selection dynamics; strict equilibrium set; Nash equilibrium component.;
    All these keywords.

    JEL classification:

    • C79 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Other

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