  We investigate mean field games for players, who are weakly coupled via their
empirical measure. To this end we investigate time-dependent pure jump type
propagators over a finite space in the framework of non-linear Markov
processes. We show that the individual optimal strategy results from a
consistent coupling of an optimal control problem with a forward non-autonomous
dynamics which leads to the well-known Mckean-Vlasov dynamics in the limit as
the number N of players goes to infinity. The case where one player has an
individual preference different to the ones of the remaining players is also
covered. The limiting system represents a 1/N-Nash Equilibrium for the
approximating system of N players.
