Evolutionary game dynamics and the analysis of agent-based imitation models: The long run, the medium run and the importance of global analysis

In this paper it is examined under which circumstances analytical concepts developed in evolutionary game theory can be usefully applied to predict the behavior of imitation processes of several interacting finite populations of agents. I review results concerning stochastic stability and approximation by deterministic dynamics in the long run and in the medium run and complement the theoretical analysis with insights obtained from simulations. In particular, it is demonstrated that the predictive power of deterministic dynamic analysis depends on the structure of the basins of attraction with respect to that dynamical system. Methods developed for the global analysis of deterministic systems turn out to be useful to characterize the predictive power of the deterministic analysis.