A uniqueness result for finite-state mean field games with non-separable Hamiltonian

Abstract

We study a class of continuous-time mean field games on a finite state space with transition rates depending on the population distribution, leading to a non-separable Hamiltonian. In this setting, classical Lasry--Lions monotonicity arguments do not apply directly. We establish a new uniqueness result on arbitrary time horizons under a combination of strong monotonicity assumptions on the costs and quantitative bounds on the interaction term in the dynamics.