In this talk we will review some recent results, obtained in collaboration with S. Hadikhanloo, about the approximation of first order, or deterministic, mean field games. We will present an approximation which can be interpreted as a mean field game in discrete time with a finite state space. Thus, the resulting approximation can be seen as a particular instance of the class of mean field games introduced by Gomes, Mohr and Souza in 2010. Next, we provide an algorithm that allows to find a numerical solution of these games, which is based on well-known "Fictitious play" method in game theory. Finally, we will show the convergence of equilibria of the finite games to an equilibria of the continuous first order mean field game and we will show some extensions of the previous approximation results.
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