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From evolutionary to strategic stability

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  • DEMICHELIS, Stefano
  • RITZBERGER, Klaus

Abstract

A component of Nash equilibria is (dynamically) potentially stable if there exists an evolutionary selection dynamics from a broad class for which the component is asymptotically stable. A necessary condition for potential stability is that the component's index agrees with its Euler characteristic. Second, if the latter is nonzero, the component contains a strategically stable set. If the Euler characteristic would be zero, the dynamics (which justifies potential stability) could be slightly perturbed so as to remove all zeros close to the component. Hence, any robustly potentially stable component contains equilibria which satisfy the strongest rationalistic refinement criteria.

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Bibliographic Info

Paper provided by Université catholique de Louvain, Center for Operations Research and Econometrics (CORE) in its series CORE Discussion Papers with number 2000059.

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Date of creation: 01 Dec 2000
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Handle: RePEc:cor:louvco:2000059

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References

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Citations

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Cited by:
  1. Dieter Balkenborg & Stefano Demichelis & Dries Vermeulen, 2010. "Where strategic and evolutionary stability depart - a study of minimal diversity games," Discussion Papers 1001, Exeter University, Department of Economics.
  2. Dieter Balkenborg & Dries Vermeulen, 2012. "Universality of Nash Components," Discussion Papers 1205, Exeter University, Department of Economics.
  3. Stefano Demichelis & Klaus Ritzberger & Jeroen M. Swinkels, 2004. "The simple geometry of perfect information games," International Journal of Game Theory, Springer, vol. 32(3), pages 315-338, 06.
  4. Jens Josephson, 2008. "Stochastic better-reply dynamics in finite games," Economic Theory, Springer, vol. 35(2), pages 381-389, May.
  5. Geir B. , Asheim & Voorneveld, Max & W. Weibull, Jörgen, 2009. "Epistemically Stable Strategy Sets," Memorandum 01/2010, Oslo University, Department of Economics.
  6. Michel Benaïm & Josef Hofbauer & Sylvain Sorin, 2012. "Perturbations of Set-Valued Dynamical Systems, with Applications to Game Theory," Dynamic Games and Applications, Springer, vol. 2(2), pages 195-205, June.
  7. Kuzmics, Christoph, 2004. "Stochastic evolutionary stability in extensive form games of perfect information," Games and Economic Behavior, Elsevier, vol. 48(2), pages 321-336, August.
  8. Demichelis, Stefano, 2012. "Evolution towards efficient coordination in repeated games, preliminary version," MPRA Paper 39311, University Library of Munich, Germany.
  9. Stefano Demichelis, 2012. "Evolution towards asymptotic efficiency, preliminary version," Quaderni di Dipartimento 173, University of Pavia, Department of Economics and Quantitative Methods.
  10. Balkenborg, Dieter & Schlag, Karl H., 2007. "On the evolutionary selection of sets of Nash equilibria," Journal of Economic Theory, Elsevier, vol. 133(1), pages 295-315, March.
  11. Demichelis, Stefano & Germano, Fabrizio, 2002. "On (un)knots and dynamics in games," Games and Economic Behavior, Elsevier, vol. 41(1), pages 46-60, October.

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