From evolutionary to strategic stability

Stefano Demichelis and Klaus Ritzberger

No 2000059, LIDAM Discussion Papers CORE from Université catholique de Louvain, Center for Operations Research and Econometrics (CORE)

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.

Date: 2000-12-01
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Journal Article: From evolutionary to strategic stability (2003)
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