In this paper we study a fully discrete Semi-Lagrangian approximation of a
second order Mean Field Game system, which can be degenerate. We prove that the
resulting scheme is well posed and, if the state dimension is equals to one, we
prove a convergence result. Some numerical simulations are provided, evidencing
the convergence of the approximation and also the difference between the
numerical results for the degenerate and non-degenerate cases.Comment: 21 pages, 8 figure