Approximation and convergence in finite state Mean Field Games

Wednesday 22 November 2017 h.14:30, Room 2BC30
Alekos Cecchin (Padova, Dip. Mat.)
“Approximation and convergence in finite state Mean Field Games"

Mean Field Games represent limit models for symmetric non-zero sum non-cooperative dynamic games, when the number N of players tend to infinity. We focus on finite time horizon problems where the position of each agent belongs to a finite state space. Relying on a probabilistic representation of the dynamics in terms of Poisson random measures, we first show that a solution of the Mean Field Game provides an approximate symmetric Nash equilibrium for the N-player game. Then, under stronger assumptions for which uniqueness holds, we prove that the sequence on Nash equilibria converges to a Mean Field Game solution. We exploit the so-called Master Equation, which in this framework is a first order quasilinear PDE stated in the symplex of probability measures.