Nonstandard finite difference treatment of a differential game problem

This paper presents and analyses some Mean Field Games (MFGs) models that depict interactions between two groups where the number of participants tends to +infinity.Solutions to differential game problems, systems of partial differential equations. MFGtheory equations have been developed to approximate the static and evolutionary versions of such models. We present numerical methods and simulations. To solve the problem in the resulting system of equations, we propose nonstandard finite difference schemes for the optimal planning problem, which has an optimal control formulation. We also conduct numerical tests. Mathematics Subject Classification: 65M06, 33F05.