A semi-Lagrangian scheme for First-Order Mean Field Games based on monotone operators
Numerical Analysis
2026-05-12 v2 Numerical Analysis
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.
Keywords
Cite
@article{arxiv.2506.10509,
title = {A semi-Lagrangian scheme for First-Order Mean Field Games based on monotone operators},
author = {Elisabetta Carlini and Valentina Coscetti},
journal= {arXiv preprint arXiv:2506.10509},
year = {2026}
}