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Evolutionary game dynamics

Authors: Josef Hofbauer and Karl Sigmund
Journal: Bull. Amer. Math. Soc. 40 (2003), 479-519
MSC (2000): Primary 91A22; Secondary 91-02, 92-02, 34D20
Published electronically: July 10, 2003
MathSciNet review: 1997349
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Abstract: Evolutionary game dynamics is the application of population dynamical methods to game theory. It has been introduced by evolutionary biologists, anticipated in part by classical game theorists. In this survey, we present an overview of the many brands of deterministic dynamical systems motivated by evolutionary game theory, including ordinary differential equations (and, in particular, the replicator equation), differential inclusions (the best response dynamics), difference equations (as, for instance, fictitious play) and reaction-diffusion systems. A recurrent theme (the so-called `folk theorem of evolutionary game theory') is the close connection of the dynamical approach with the Nash equilibrium, but we show that a static, equilibrium-based viewpoint is, on principle, unable to always account for the long-term behaviour of players adjusting their behaviour to maximise their payoff.

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Additional Information

Josef Hofbauer
Affiliation: (Hofbauer) Institut für Mathematik, Universität Wien, Strudlhofgasse 4, A-1090 Vienna, Austria

Karl Sigmund
Affiliation: (Sigmund) Institut für Mathematik, Universität Wien, Strudlhofgasse 4, A-1090 Vienna, Austria; (Sigmund) IIASA, A-2361 Laxenburg, Austria

Received by editor(s): March 7, 2003
Received by editor(s) in revised form: April 12, 2003
Published electronically: July 10, 2003
Article copyright: © Copyright 2003 American Mathematical Society