Approximation of stable solutions to second order mean field game systems

We expose a general framework for the study of numerical approximations of a certain class of solutions, called stable solutions, of second order mean-field game systems for which uniqueness of solutions is not guaranteed. To illustrate the approach, we focus on a very simple example of stationary second-order MFG system. We then re-express the solutions of the system as zeros of a well chosen nonlinear map and establish the fact that stable solutions are regular points of this map. This fact is then used to study the finite element approximations of solutions and the local convergence of Newton’s method.

Durham Symposium on Mean Field Games

Durham University