Mean field games of controls: Finite difference approximations

We consider a class of mean field games in which the agents interact through both their states and controls, we focus on situations generic agent tries to adjust her speed (control) an average (the is made neighborhood state space). In such cases, monotonicity assumptions that are frequently theory do not hold, uniqueness cannot be expected general. Such model lead systems forward-backward nonlinear nonlocal parabolic equations; latter supplemented with various kinds boundary conditions, particular Neumann-like conditions stemming from reflection underlying controled stochastic processes. The present work deals numerical approximations above megntioned systems. After describing finite difference scheme, propose iterative method for solving equations arise discrete setting; it combines continuation method, Newton iterations inner loops bigradient like solver. used simulating two examples. also make experiments behaviour algorithm when parameters vary.