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

Approximation of deterministic mean field games under polynomial growth conditions on the data