International audienceIn this work we propose a fully discrete semi-Lagrangian scheme for a first order mean field game system. We prove that the resulting discretization admits at least one solution and, in the scalar case, we prove a convergence result for the scheme. Numerical simulations and examples are also discussed

Abstract-In this work we consider first and second order Mean Field Games (MFGs) systems, introduced in [18], [19], [20]. For the first order case, we recall a fully-discrete SemiLagrangian (SL) scheme introduced in [9] and its main properties. We propose the natural extension of this scheme for the second order case and we present some numerical simulations.