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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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    Citations

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    Cited by:

    1. Matthijs van Veelen, 2010. "But Some Neutrally Stable Strategies are More Neutrally Stable than Others," Tinbergen Institute Discussion Papers 10-033/1, Tinbergen Institute.
    2. Sjaak Hurkens & Karl H. Schlag, 1999. "Communication, coordination and efficiency in evolutionary one-population models," Economics Working Papers 387, Department of Economics and Business, Universitat Pompeu Fabra.
    3. van Veelen, Matthijs, 2012. "Robustness against indirect invasions," Games and Economic Behavior, Elsevier, vol. 74(1), pages 382-393.
    4. De Jaegher, Kris, 2008. "Efficient communication in the electronic mail game," Games and Economic Behavior, Elsevier, vol. 63(2), pages 468-497, July.
    5. Abreu, Dilip & Sethi, Rajiv, 2003. "Evolutionary stability in a reputational model of bargaining," Games and Economic Behavior, Elsevier, vol. 44(2), pages 195-216, August.
    6. Karl H. Schlag, "undated". "When Does Evolution Lead to Efficiency in Communication Games?," ELSE working papers 026, ESRC Centre on Economics Learning and Social Evolution.
    7. Karl H. Schlag, 1994. "Evolution in Partnership Games,an Equivalence Result," Discussion Paper Serie B 298, University of Bonn, Germany.
    8. Karl H. Schlag, "undated". "When Does Evolution Lead to Efficiency in Communication Games?," ELSE working papers 026, ESRC Centre on Economics Learning and Social Evolution.
    9. Kris De Jaegher, 2008. "The evolution of Horn's rule," Journal of Economic Methodology, Taylor & Francis Journals, vol. 15(3), pages 275-284.
    10. Matthijs van Veelen & Julian Garcia, 2012. "In and out of Equilibrium II: Evolution in Repeated Games with Discounting and Complexity Costs," Tinbergen Institute Discussion Papers 12-089/I, Tinbergen Institute.
    11. Rota Bulò, Samuel & Bomze, Immanuel M., 2011. "Infection and immunization: A new class of evolutionary game dynamics," Games and Economic Behavior, Elsevier, vol. 71(1), pages 193-211, January.
    12. Sandholm, William H., 2015. "Population Games and Deterministic Evolutionary Dynamics," Handbook of Game Theory with Economic Applications, Elsevier.
    13. Norman, Thomas W.L., 2008. "Dynamically stable sets in infinite strategy spaces," Games and Economic Behavior, Elsevier, vol. 62(2), pages 610-627, March.
    14. Lars Koch, 2008. "Evolution and Correlated Equilibrium," Bonn Econ Discussion Papers bgse14_2008, University of Bonn, Germany.
    15. García, Julián & van Veelen, Matthijs, 2016. "In and out of equilibrium I: Evolution of strategies in repeated games with discounting," Journal of Economic Theory, Elsevier, vol. 161(C), pages 161-189.

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