  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.

Probability