A fully-discrete Semi-Lagrangian scheme for a first order mean field   game problem
  In this work we propose a fully-discrete Semi-Lagrangian scheme for a {\it 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. 
E. Carlini and F. J. Silva
math.NA