Numerical Solution of Mean Field Problem with Limited Management Resource

The paper presents a computational algorithm for solving problem formulated in terms of Mean Field Game theory with limited management resource. The Mean Field equilibrium leads to a coupled system of two parabolic partial differential equations: Fokker–Planck–Kolmogorov and Hamilton–Jacobi–Bellman ones with an additional constraint in the form of the inequality. The article is devoted to the discrete approximation of these equations and reformulating the discrete statement in the form of the saddle point problem with the condition of complementary slackness. An iterative algorithm is presented for solving the obtained discrete problem with justification of the convergence of its elements. The convergence of the algorithm as a whole is illustrated by a numerical example.