  We investigate mean-field games from the point of view of a large number of
indistinguishable players which eventually converges to infinity. The players
are weakly coupled via their empirical measure. The dynamics of the states of
the individual players is governed by a non-autonomous pure jump type semi
group in a Euclidean space, which is not necessarily smoothing. Investigations
are conducted 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. In the limit as the
number $N$ of players goes to infinity this leads to a jump-type analog of the
well-known non-linear McKean-Vlasov dynamics. The case where one player has an
individual preference different from the ones of the remaining players is also
covered. The two results combined reveal an epsilon-Nash Equilibrium for the
$N$-player games.
