  The paper is concerned with the deterministic limit of mean field games with
the nonlocal coupling. It is assumed that the dynamics of mean field games are
given by nonlinear Markov processes. This type of games includes stochastic
mean field games as well as mean field games with finite state space. We
consider the limiting deterministic mean field game within the framework of
minimax approach. The concept of minimax solutions is close to the
probabilistic formulation. In this case the Hamilton--Jacobi equation is
considered in the minimax/viscosity sense, whereas the flow of probabilities is
determined by the probability on the set of solutions of the differential
inclusion associated with the Hamilton-Jacobi equation such that those
solutions are viable in the graph of the minimax solution. The main result of
the paper is the convergence (up to subsequence) of the solutions of the mean
field games to the minimax solution of deterministic mean field game in the
case when the underlying dynamics converge to the deterministic evolution.
