No . 84 A Result for Approximation of Imitational Behavior in Large Populations

This paper rigorously justifies the approximation of aggregate imitational behavior in large populations by the deterministic dynamics given by Bjönerstedt and Weibull. We first clarify what models fit their formulation, in which the stochastic dynamics depends only on the average frequencies of strategies in populations. Then we show that the stochastic process of each individual’s behavior converges to a common McKean process and the average frequencies come to represent the deterministic dynamics of Bjönerstedt and Weibull when the number of individuals goes to infinity. Another derivation of replicator dynamics is also given by application to specific models of imitational behavior. JEL classification: C72,C73.