From evolutionary to strategic stability |
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Authors: | Stefano Demichelis |
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Institution: | a University of Pavia and CORE, 34, Voie du Roman Pays, B-1348 Louvain-la-Neuve, Belgium b Department of Economics and Finance, Institute for Advanced Studies, Stumpergasse 56, A-1060 Vienna, Austria |
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Abstract: | A connected component of Nash equilibria is (dynamically) potentially stable if there exits 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 (that 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 that satisfy the strongest rationalistic refinement criteria. |
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Keywords: | C72 |
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