  We consider a deterministic mean field games problem in which a typical agent
solves an optimal control problem where the dynamics is affine with respect to
the control and the cost functional has a growth which is polynomial with
respect to the state variable. In this framework, we construct a mean field
game problem in discrete time and finite state space that approximates
equilibria of the original game. Two numerical examples, solved with the
fictitious play method, are presented.
