Discrete approximation of stationary Mean Field Games

In this paper, we focus on stationary (ergodic) mean-field games (MFGs). These arise in the study of long-time behavior finite-horizon MFGs. Motivated by a prior scheme for Hamilton–Jacobi equations introduced Aubry–Mather's theory, introduce discrete approximation to Relying Kakutani's fixed-point theorem, prove existence and uniqueness (up additive constant) solutions problem. Moreover, show that problem converge, uniformly nonlocal case weakly local case, classical