title: Transition matrix model for evolutionary game dynamics.
abstract: 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.
authors.affiliation: Department of Mathematics, University of Pittsburgh, Pittsburgh, Pennsylvania 15260, USA.
authors.forename: G Bard
authors.initials: GB
authors.lastname: Ermentrout
authors.affiliation: Mathematics Department, United States Naval Academy, Annapolis, Maryland 21402, USA.
authors.forename: Christopher
authors.initials: C
authors.lastname: Griffin
authors.affiliation: Department of Mathematics, Pennsylvania State University, University Park, Pennsylvania 16802, USA.
authors.forename: Andrew
authors.initials: A
authors.lastname: Belmonte