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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:

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    2. Lucas Pahl, 2022. "Polytope-form games and Index/Degree Theories for Extensive form games," Papers 2201.02098, arXiv.org, revised Jan 2023.
    3. Geir B. Asheim & Mark Voorneveld & Jörgen W. Weibull, 2016. "Epistemically Robust Strategy Subsets," Games, MDPI, vol. 7(4), pages 1-16, November.
    4. Balkenborg, Dieter & Vermeulen, Dries, 2014. "Universality of Nash components," Games and Economic Behavior, Elsevier, vol. 86(C), pages 67-76.
    5. Stefano Demichelis, 2012. "Evolution towards asymptotic efficiency, preliminary version," Quaderni di Dipartimento 173, University of Pavia, Department of Economics and Quantitative Methods.
    6. 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.
    7. 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.
    8. Peter Wikman, 2022. "Nash blocks," International Journal of Game Theory, Springer;Game Theory Society, vol. 51(1), pages 29-51, March.
    9. Mertikopoulos, Panayotis & Sandholm, William H., 2018. "Riemannian game dynamics," Journal of Economic Theory, Elsevier, vol. 177(C), pages 315-364.
    10. Demichelis, Stefano, 2012. "Evolution towards efficient coordination in repeated games, preliminary version," MPRA Paper 39311, University Library of Munich, Germany.
    11. 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.
    12. Demichelis, Stefano & Germano, Fabrizio, 2002. "On (un)knots and dynamics in games," Games and Economic Behavior, Elsevier, vol. 41(1), pages 46-60, October.
    13. 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.
    14. Jacob K. Goeree & Philippos Louis, 2021. "M Equilibrium: A Theory of Beliefs and Choices in Games," American Economic Review, American Economic Association, vol. 111(12), pages 4002-4045, December.
    15. Srihari Govindan & Rida Laraki & Lucas Pahl, 2020. "On Sustainable Equilibria," Post-Print hal-03767987, HAL.
    16. 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.
    17. Sandholm, William H., 2015. "Population Games and Deterministic Evolutionary Dynamics," Handbook of Game Theory with Economic Applications,, Elsevier.
    18. 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.
    19. 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.
    20. 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.
    21. Jason Milionis & Christos Papadimitriou & Georgios Piliouras & Kelly Spendlove, 2022. "Nash, Conley, and Computation: Impossibility and Incompleteness in Game Dynamics," Papers 2203.14129, arXiv.org.
    22. 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.
    23. 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.
    24. Geir B. , Asheim & Voorneveld, Max & W. Weibull, Jörgen, 2009. "Epistemically Stable Strategy Sets," Memorandum 01/2010, Oslo University, Department of Economics.
    25. Reuben Bearman, 2023. "Signaling Games with Costly Monitoring," Papers 2302.01116, arXiv.org.

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