A semi-Lagrangian scheme for First-Order Mean Field Games based on monotone operators

2025/06/12 by Carlini, Elisabetta, Coscetti, Valentina · 2 citations
#35Q89 #49N80 #65M12 #65M25 #91A16 #FOS: Mathematics #Numerical Analysis (math.NA)

paper · doi:10.48550/arxiv.2506.10509

Abstract

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.

Cited by

• Newton methods for mean field games: A numerical study
• Newton Methods for Mean Field Games: A Numerical Study

Related

• A fully-discrete Semi-Lagrangian scheme for a first order mean field game problem
• A Lagrange-Galerkin scheme for first order mean field games systems
• A high-order scheme for mean field games
• A Fully-discrete Semi-Lagrangian scheme for a price formation MFG model
• An introduction to monotonicity methods in mean-field games