Semi-Lagrangian schemes for mean field game models

Abstract

In this work we consider first and second order Mean Field Games (MFGs) systems, introduced in \cite{LasryLions06i,LasryLions06ii,LasryLions07}. For the first order case, we recall a fully-discrete Semi-Lagrangian (SL) scheme introduced in \cite{CS12} and its main properties. We propose the natural extension of this scheme for the second order case and we present some numerical simulations