Adaptive dynamics in games played by heterogeneous populations

Consider a population of agents who play a game through repeated interactions, and adapt their behavior based on information about other agents' previous behavior. The standard way of modeling such a process is to assume that everyone in the population is governed by the same adaptive rule, e.g., best response, imitation, or the replicator dynamic. This paper studies heterogeneous populations of agents in which some agents are best responders, others are conformists (they do what the majority does), and still others are nonconformists (they do the opposite of what the majority does). Unlike deterministic best reply processes, which in 2x2 games converge to Nash equilibrium, these heterogeneous processes may have limit cycles; moreover limit cycles may exist even when the proportion of non best responders is arbitrarily small. We show how to analyze the asymptotic behavior of such processes through a suitable generalization of Bendixson stability theory combined with stochastic approximation theory