A semi-Lagrangian scheme for First-Order Mean Field Games based on monotone operators
Provides a convergent numerical scheme for non-local Mean Field Games, benefiting researchers in game theory and PDEs.
The paper develops a semi-Lagrangian scheme for first-order Mean Field Games, proving convergence to weak solutions via monotonicity, and introduces an accelerated Policy Iteration method that significantly improves computational performance.
We construct a semi-Lagrangian scheme for first-order, time-dependent, and non-local Mean Field Games. The convergence of the scheme to a weak solution of the system is analyzed by exploiting a key monotonicity property. To solve the resulting discrete problem, we implement a Learning Value Algorithm, prove its convergence, and propose an acceleration strategy based on a Policy iteration method. Finally, we present numerical experiments that validate the effectiveness of the proposed schemes and show that the accelerated version significantly improves performance.