In this work, we consider a first order mean field games system with non-local couplings. A Lagrange-Galerkin scheme for the continuity equation, coupled with a semi-Lagrangian scheme for the Hamilton-Jacobi-Bellman equation, is proposed to discretize the mean field games system. The convergence of solutions to the scheme towards a solution to the mean field game system is established in arbitrary space dimensions. The scheme is implemented to approximate two mean field games systems in dimension one and two.

翻译：本文考虑一类具有非局部耦合的一阶平均场博弈系统。针对连续性方程提出拉格朗日-伽辽金格式，并与哈密顿-雅可比-贝尔曼方程的半拉格朗日格式相结合，对平均场博弈系统进行离散化。在任意空间维度上证明了该格式的解收敛于平均场博弈系统的解。该格式被用于逼近一维和二维空间中的两个平均场博弈系统。