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Nash™s three proofs for the existence of equilibria in strategic games correspond to three dynamics: The best re- sponse dynamics (equivalent to Brown™s fictitious play), the smoothed best response dynamics, and the Brown&von Neumann&Nash dynamics. We prove that an equilibrium which is evolutionarily stable as defined by Maynard Smith is (globally) asymptotically stable for each of these three dynamics.

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  • Hofbauer, J. and Sigmund, K. (1998): Evolutionary Games and Population Dynamics. Cambridge University Press.

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  • Hopkins, E. (1999): A note on best response dynamics. Games Econ. Behav.29: 138-150.

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  • Hofbauer, J. (1995): Stability for the Best Response Dynamics. Preprint.

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Selection
Language English
Year of
Foundation
2001
Publication
Programme
ceased
Publisher Akadémiai Kiadó
Publisher's
Address
H-1117 Budapest, Hungary 1516 Budapest, PO Box 245.
Responsible
Publisher
Chief Executive Officer, Akadémiai Kiadó
ISSN 1585-1931 (Print)
ISSN 1588-287X (Online)