Numerical solution of mean-field game problem with an external control

The paper presents a computational algorithm for solving an optimal control problem formulated in terms of mean-field game theory. The equilibrium of the mean field leads to a coupled system of two parabolic partial differential equations: Fokker-Plank-Kolmogorov and Hamilton-Jacobi-Bellman ones. We extend the conventional model by incorporating a mechanism for external (crisis) influence on the behavior of agents. The article is devoted to the discrete approximation of such a differential statement. The constructed algorithm is implemented to the task of heating insulation of houses.