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Evolutionarily stable sets

Author

Listed:
  • Karl H. Schlag

    (Department of Economics, European University Institute, Badia Fiesolana, Via dei Roccettini 9, I-50016 San Domenico di Fiesole , Italy)

  • Dieter Balkenborg

    (Department of Economics, University of Exeter, Streatham Court, Exeter EX4 4PU, U.K.)

Abstract

This paper provides definitions for the evolutionary stability of sets of strategies based on simple fitness comparisons in the spirit of the definition of an evolutionarily stable strategy (ESS) by Taylor and Jonker (1978). It compares these with the set-valued notions of Thomas (1985d) and Swinkels (1992). Provided only that the fitness function is analytic, our approach yields an alternative characterization of Thomas' evolutionarily stable sets (ES Sets) which does not rely on the structure or topology of the underlying strategy space. Moreover, these sets are shown to have a very special geometric structure and to be finite in number. For bimatrix games ES Sets are shown to be more uniformly robust against mutations than apparent from the definition and hence to be equilibrium evolutionarily stable sets in the sense of Swinkels (1992).

Suggested Citation

  • Karl H. Schlag & Dieter Balkenborg, 2001. "Evolutionarily stable sets," International Journal of Game Theory, Springer;Game Theory Society, vol. 29(4), pages 571-595.
    • Handle: RePEc:spr:jogath:v:29:y:2001:i:4:p:571-595
    Note: Received November 1995/Final version December 2000
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