Abstract
Evolutionary games constitute the most recent major mathematical tool for understanding, modelling and predicting evolution in biology and other fields. They complement other well establlished tools such as branching processes and the Lotka-Volterra (1910) equations (e.g. for the predator - prey dynamics or for epidemics evolution). Evolutionary Games also brings novel features to game theory. First, it focuses on the dynamics of competition rather than restricting attention to the equilibrium. In particular, it tries to explain how an equilibrium emerges. Second, it brings new definitions of stability, that are more adapted to the context of large populations. Finally, in contrast to standard game theory, players are not assumed to be “rational” or “knowledgeable” as to anticipate the other players’ choices. The objective of this article, is to present foundations as well as recent advances in evolutionary games, highlight the novel concepts that they introduce with respect to game theory as formulated by John Nash, and describe through several examples their huge potential as tools for modeling interactions in complex systems.
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