Computation of Mean-Field Equilibria with Correlated Stochastic Processes

Abstract

he numerical algorithm is presented for solving differential problem formulated as the Mean-Field Game (MFG) with the coupled system of two parabolic partial differential equations: the Fokker-Plank-Kolmogorov equation and the Hamilton-Jacobi-Bellman one. The case is considered with correlation of the considered stochastic processes. The description focuses on the discrete semi-Lagrangian approximation of these equations and on the application of the MFG theory directly at discrete level. The constructed algorithm is implemented to the problem of carbon dioxide pollution as an illustration