ncts

The mean field games (MFGs) consist of a coupled system of nonlinear partial differential equations, which describe the evolution of the density distribution of agents (player) through the Fokker--Planck(FP) equation and the evolution of the control inputs of agents through the Hamilton--Jacobi--Bellman (HJB) equation. Moreover, the initial condition is imposed on the FP equation, and the terminal condition on the HJB equation. Therefore, the system is in the form of a space-time boundary value problem. MFGs have found applications in various fields, such as crowd control and control of autonomous vehicle fleets, as well as mathematical biology, engineering, economics, and so on. In this talk, we introduce an implementation-friendly numerical scheme recently proposed by us, which combines linearization via the Cole-Hopf transformation and fictitious-play iterations. Furthermore, we prove the convergence of the scheme and examine its validity through numerical.