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On the Dynamic Foundation of Evolutionary Stability in Continuous Models

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  • Jörg Oechssler
  • Frank Riedel

Abstract

We show in this paper that none of the existing static evolutionary stability concepts (ESS, CSS, uninvadability, NIS) is sufficient to guarantee dynamic stability in the weak topology with respect to standard evolutionary dynamics if the strategy space is continuous. We propose a new concept, evolutionary robustness, which is stronger than the previous concepts. Evolutionary robustness ensures dynamic stability for replicator dynamics in doubly symmetric games.

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File URL: http://www.wiwi.uni-bonn.de/bgsepapers/bonedp/bgse7_2000.pdf
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Bibliographic Info

Paper provided by University of Bonn, Germany in its series Bonn Econ Discussion Papers with number bgse7_2000.

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Date of creation: Jul 2000
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Handle: RePEc:bon:bonedp:bgse7_2000

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Postal: Bonn Graduate School of Economics, University of Bonn, Adenauerallee 24 - 26, 53113 Bonn, Germany
Fax: +49 228 73 6884
Web page: http://www.bgse.uni-bonn.de

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Keywords: replicator dynamics; evolutionary stability; ESS; CSS;

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  1. Bester, Helmut & Guth, Werner, 1998. "Is altruism evolutionarily stable?," Journal of Economic Behavior & Organization, Elsevier, vol. 34(2), pages 193-209, February.
  2. J. Maynard Smith, 2010. "The Theory of Games and Evolution of Animal Conflicts," Levine's Working Paper Archive 448, David K. Levine.
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