Evolutionary Games in Finite Populations

Evolutionary dynamics is based on mutation, selection and random drift. When the success of a certain type depends on others, game-theoretic approaches are more appropriate than optimization arguments.

Traditionally, evolutionary game theory considers infinitely large populations, where stochastic effects can be neglected. Only recently, stochastic processes have been applied to model evolutionary game dynamics in finite populations analytically. In this context, analytical results are obtained that can be very different from the usual results of the replicator dynamics.

After a general introduction to evolutionary game theory, I will discuss these stochastic approaches. It will be shown that the connection to the traditional approaches based on the replicator dynamics can be obtained by an approximation for large populations. As applications of evolutionary game dynamics, I will discuss mechanisms for the evolution of cooperation and for the emergence of punishment.