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Exploration Noise for Learning Linear-Quadratic Mean Field Games

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  • François Delarue

    (CNRS, LJAD, Université Côte d’Azur, 06108 Nice Cedex 2, France)

  • Athanasios Vasileiadis

    (CNRS, LJAD, Université Côte d’Azur, 06108 Nice Cedex 2, France)

Abstract

The goal of this paper is to demonstrate that common noise may serve as an exploration noise for learning the solution of a mean field game. This concept is here exemplified through a toy linear-quadratic model, for which a suitable form of common noise has already been proven to restore existence and uniqueness. We here go one step further and prove that the same form of common noise may force the convergence of the learning algorithm called fictitious play, and this without any further potential or monotone structure. Several numerical examples are provided to support our theoretical analysis.

Suggested Citation

  • François Delarue & Athanasios Vasileiadis, 2025. "Exploration Noise for Learning Linear-Quadratic Mean Field Games," Mathematics of Operations Research, INFORMS, vol. 50(3), pages 1762-1831, August.
    • Handle: RePEc:inm:ormoor:v:50:y:2025:i:3:p:1762-1831
    DOI: 10.1287/moor.2021.0157
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