Multiagent models in time-varying and random environment

In this paper we study multiagent models with time-varying type change. Assume that there exist a closed system of $N$ agents classified into $r$ types according to their states of an internal system; each agent changes its type by an internal dynamics of the internal states or by the relative frequency of different internal states among the others, e.g., multinomial sampling. We investigate the asymptotic behavior of the empirical distributions of the agents' types as $N$ goes to infinity, by the weak convergence criteria for time-inhomogeneous Markov processes and the theory of Volterra integral equations of the second kind. We also prove convergence theorems of these models evolving in random environment.