Adaptive dynamics in games played by heterogeneous populations

Consider a population of agents who play a game through repeated interactio ns, and adapt their behavior based on information about other agents' previ ous 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., be st response, imitation, or the replicator dynamic. This paper studies heter ogeneous populations of agents in which some agents are best responders, ot hers are conformists (they do what the majority does), and still others are nonconformists (they do the opposite of what the majority does). Unlike de terministic best reply processes, which in 2 x 2 games converge to Nash equ ilibrium, these heterogeneous processes may have limit cycles; moreover lim it cycles may exist even when the proportion of non best responders is arbi trarily small. We show how to analyze the asymptotic behavior of such proce sses through a suitable generalization of Bendixson stability theory combin ed with stochastic approximation theory. Journal of Economic Literature Cla ssification Numbers: C44 C73, D83. (C) 2000 Academic Press.