slides

An ergodic problem for Mean Field Games: qualitative properties and numerical simulations

Abstract

This paper is devoted to some qualitative descriptions and some numerical results for ergodic Mean Field Games systems which arise, e.g., in the homogenization with a small noise limit. We shall consider either power type potentials or logarithmic type ones. In both cases, we shall establish some qualitative properties of the effective Hamiltonian Hˉ\bar H and of the effective drift bˉ\bar b. In particular we shall provide two cases where the effective system keeps/looses the Mean Field Games structure, namely where ∇PHˉ(P,α)\nabla_P \bar H(P,\alpha) coincides or not with bˉ(P,α)\bar b(P, \alpha). On the other hand, we shall provide some numerical tests validating the aforementioned qualitative properties of Hˉ\bar H and bˉ\bar b. In particular, we provide a numerical estimate of the discrepancy ∇PHˉ(P,α)−bˉ(P,α)\nabla_P \bar H(P,\alpha)-\bar b(P, \alpha)

    Similar works