International Journal of Game Theory

, Volume 29, Issue 4, pp 571–595

Evolutionarily stable sets

  • Dieter Balkenborg
  • Karl H. Schlag


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).

Key words: evolutionary stability equilibrium components 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • Dieter Balkenborg
    • 1
  • Karl H. Schlag
    • 2
  1. 1.Department of Economics, University of Exeter, Streatham Court, Exeter EX4 4PU, U.K. (e-mail:
  2. 2.Department of Economics, European University Institute, Badia Fiesolana, Via dei Roccettini 9, I-50016 San Domenico di Fiesole (FI), Italy (e-mail:

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