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arXiv · 2506.10509

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

Elisabetta Carlini·Valentina Coscetti
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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.

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Elisabetta Carlini, Valentina Coscetti. 2025-06-12. A semi-Lagrangian scheme for First-Order Mean Field Games based on monotone operators. https://arxiv.org/abs/2506.10509

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