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Evolutionarily stable sets

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Author Info

  • 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).

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Bibliographic Info

Article provided by Springer in its journal International Journal of Game Theory.

Volume (Year): 29 (2001)
Issue (Month): 4 ()
Pages: 571-595

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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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Related research

Keywords: evolutionary stability · equilibrium components;

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Cited by:
  1. 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.
  2. Karl H. Schlag, 1994. "When Does Evolution Lead to Efficiency in Communication Games?," Discussion Paper Serie B 299, University of Bonn, Germany.
  3. Dilip Abreu & Rajiv Sethi, 2001. "Evolutionary Stability in a Reputational Model of Bargaining," Game Theory and Information 0103001, EconWPA.
  4. K.J.M. De Jaegher, 2007. "The evolution of Horn's rule," Working Papers 07-12, Utrecht School of Economics.
  5. Thomas Norman, 2005. "Dynamically Stable Sets in Infinite Strategy Spaces," Economics Series Working Papers 251, University of Oxford, Department of Economics.
  6. Karl H. Schlag, 1994. "Evolution in Partnership Games,an Equivalence Result," Discussion Paper Serie B 298, University of Bonn, Germany.
  7. 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.
  8. Lars Koch, 2008. "Evolution and Correlated Equilibrium," Bonn Econ Discussion Papers bgse14_2008, University of Bonn, Germany.
  9. K.J.M. De Jaegher, 2007. "Efficient communication in the electronic mail game," Working Papers 07-11, Utrecht School of Economics.
  10. 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.
  11. Matthijs van Veelen, 2010. "But Some Neutrally Stable Strategies are More Neutrally Stable than Others," Tinbergen Institute Discussion Papers 10-033/1, Tinbergen Institute.
  12. 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.
  13. van Veelen, Matthijs, 2012. "Robustness against indirect invasions," Games and Economic Behavior, Elsevier, vol. 74(1), pages 382-393.

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