Transition matrix model for evolutionary game dynamics.
We study an evolutionary game model based on a transition matrix approach, in which the total change in the proportion of a population playing a given strategy is summed directly over contributions from all other strategies. This general approach combines aspects of the traditional replicator model, such as preserving unpopulated strategies, with mutation type dynamics, which allow for nonzero switching to unpopulated strategies, in terms of a single transition function. Under certain conditions, this model yields an endemic population playing non Nash equilibrium strategies. In addition, a Hopf bifurcation with a limit cycle may occur in the generalized rock scissors paper game, unlike the replicator equation. Nonetheless, many of the Folk Theorem results are shown to hold for this model.
Physical review. E