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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.

Suggested Citation

  • DEMICHELIS, Stefano & RITZBERGER, Klaus, 2000. "From evolutionary to strategic stability," LIDAM Discussion Papers CORE 2000059, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  • Handle: RePEc:cor:louvco:2000059
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    Cited by:

    1. Balkenborg, Dieter & Vermeulen, Dries, 2014. "Universality of Nash components," Games and Economic Behavior, Elsevier, vol. 86(C), pages 67-76.
    2. Stefano Demichelis, 2012. "Evolution towards asymptotic efficiency, preliminary version," Quaderni di Dipartimento 173, University of Pavia, Department of Economics and Quantitative Methods.
    3. Mertikopoulos, Panayotis & Sandholm, William H., 2018. "Riemannian game dynamics," Journal of Economic Theory, Elsevier, vol. 177(C), pages 315-364.
    4. Demichelis, Stefano, 2012. "Evolution towards efficient coordination in repeated games, preliminary version," MPRA Paper 39311, University Library of Munich, Germany.
    5. Demichelis, Stefano & Germano, Fabrizio, 2002. "On (un)knots and dynamics in games," Games and Economic Behavior, Elsevier, vol. 41(1), pages 46-60, October.
    6. Balkenborg, Dieter & Vermeulen, Dries, 2019. "On the topology of the set of Nash equilibria," Games and Economic Behavior, Elsevier, vol. 118(C), pages 1-6.
    7. 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.
    8. Stefano Demichelis & Klaus Ritzberger & Jeroen M. Swinkels, 2004. "The simple geometry of perfect information games," International Journal of Game Theory, Springer;Game Theory Society, vol. 32(3), pages 315-338, June.
    9. Dieter Balkenborg & Dries Vermeulen, 2016. "Where Strategic and Evolutionary Stability Depart—A Study of Minimal Diversity Games," Mathematics of Operations Research, INFORMS, vol. 41(1), pages 278-292, February.
    10. Geir B. , Asheim & Voorneveld, Max & W. Weibull, Jörgen, 2009. "Epistemically Stable Strategy Sets," Memorandum 01/2010, Oslo University, Department of Economics.
    11. Stefano Demichelis & Amrita Dhillon, 2010. "Learning in Elections and Voter Turnout," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 12(5), pages 871-896, October.
    12. Srihari Govindan & Rida Laraki & Lucas Pahl, 2020. "On Sustainable Equilibria," Papers 2005.14094, arXiv.org, revised Aug 2021.
    13. Norman, Thomas W.L., 2018. "Inefficient stage Nash is not stable," Journal of Economic Theory, Elsevier, vol. 178(C), pages 275-293.
    14. Geir B. Asheim & Mark Voorneveld & Jörgen W. Weibull, 2016. "Epistemically Robust Strategy Subsets," Games, MDPI, Open Access Journal, vol. 7(4), pages 1-16, November.
    15. 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.
    16. Hefti, Andreas, 2016. "On the relationship between uniqueness and stability in sum-aggregative, symmetric and general differentiable games," Mathematical Social Sciences, Elsevier, vol. 80(C), pages 83-96.
    17. 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.
    18. Sandholm, William H., 2015. "Population Games and Deterministic Evolutionary Dynamics," Handbook of Game Theory with Economic Applications,, Elsevier.
    19. Xiao Luo & Xuewen Qian & Yang Sun, 2021. "The algebraic geometry of perfect and sequential equilibrium: an extension," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 71(2), pages 579-601, March.
    20. Jens Josephson, 2008. "Stochastic better-reply dynamics in finite games," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 35(2), pages 381-389, May.

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