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Evolutionary game dynamics. (English) Zbl 1049.91025

Summary: 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.

MSC:

91A22 Evolutionary games
91-02 Research exposition (monographs, survey articles) pertaining to game theory, economics, and finance
92-02 Research exposition (monographs, survey articles) pertaining to biology
34D20 Stability of solutions to ordinary differential equations
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