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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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    References listed on IDEAS

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