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arXiv · 2503.16220

A Mean Field Game System and a Related Deterministic Optimal Control Problem

Stefana-Lucia Anita
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Abstract

This paper concerns a Mean Field Game (MFG) system related to a Nash type equilibrium for dynamical games associated to large populations. One shows that the MFG system may be viewed as the Euler-Lagrange system for an optimal control problem related to a Fokker-Planck equation with control in the drift. One derives the existence of a weak solution to the MFG system and under more restrictive assumptions one proves a uniqueness result.

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Stefana-Lucia Anita. 2025-03-20. A Mean Field Game System and a Related Deterministic Optimal Control Problem. https://arxiv.org/abs/2503.16220

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