Evolutionary games: the Darwin connection

Evolutionary game theory has been introduced essentially by biologists in the seventies and has immediately diffused into economical and sociological circles. Today, it is a main pillar of the whole edifice of game theory and widely used both in theory and in applications. This tutorial aims at presenting evolutionary game theory in an easy, yet rigorous way, and to relate it with other approaches in game theory. The material presented does not require a previous acquaintance with standard game theory: these fundamentals will be developed in the first part of the tutorial, which is self-contained. In the second part the main concepts of the evolutionary and dynamical approach will be introduced, namely the concept of an evolutionarily stable strategy and the replicator dynamics. The analogies between Nash equilibria, evolutionarily stable strategies, and rest points of the dynamics will be explained. The concept of strategy errors and stochastically stable states as well as the relationships with mean dynamics and stability in the long run will also be briefly introduced. The main ideas will be illustrated using simple well known paradigmatic games such as the Prisoner's Dilemma, Hawks and Doves, and coordination games among others. Finally, some recent exciting trends in evolutionary games on networks will be introduced and discussed.