A dynamical characterization of evolutionarily stable states |
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Authors: | Immanuel M Bomze Eric E C van Damme |
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Institution: | (1) Department for Statistics and Computer Science, University of Vienna, Universitätsstrasse 5, A-1010 Wien, Austria;(2) CentER, Tilburg University, P.O. Box 90153, NL-5000 LE Tilburg, The Netherlands |
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Abstract: | Evolutionary stability, the central solution concept in evolutionary game theory, is closely related to local asymptotic stability in a certain nonlinear dynamical system operating on the state space, the so-called "replicator dynamics". However, a purely dynamical characterization of evolutionary stability is not available in an elementary manner. This characterization can be achieved by investigating so-called "derived games" which consist of mixed strategies corresponding to successful states in the original game. Using well-known facts, several characterization results are obtained within this context. These also may shed light on the extremality properties of evolutionary stability. |
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Keywords: | Asymptotic stability evolutionary games mixed strategies polymorphisms replicator dynamics stable sets |
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