Zusammenfassung
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.
Nutzer