# Fictitious Play for Mean Field Games: Continuous Time Analysis and Applications

1 Scool - Scool
Inria Lille - Nord Europe, CRIStAL - Centre de Recherche en Informatique, Signal et Automatique de Lille - UMR 9189
2 SEQUEL - Sequential Learning
Inria Lille - Nord Europe, CRIStAL - Centre de Recherche en Informatique, Signal et Automatique de Lille - UMR 9189
Abstract : In this paper, we deepen the analysis of continuous time Fictitious Play learning algorithm to the consideration of various finite state Mean Field Game settings (finite horizon, $\gamma$-discounted), allowing in particular for the introduction of an additional common noise. We first present a theoretical convergence analysis of the continuous time Fictitious Play process and prove that the induced exploitability decreases at a rate $O(\frac{1}{t})$. Such analysis emphasizes the use of exploitability as a relevant metric for evaluating the convergence towards a Nash equilibrium in the context of Mean Field Games. These theoretical contributions are supported by numerical experiments provided in either model-based or model-free settings. We provide hereby for the first time converging learning dynamics for Mean Field Games in the presence of common noise.
Document type :
Preprints, Working Papers, ...
Domain :

https://hal.inria.fr/hal-02931977
Contributor : Sarah Perrin Connect in order to contact the contributor
Submitted on : Monday, September 7, 2020 - 1:58:02 PM
Last modification on : Tuesday, January 4, 2022 - 6:51:15 AM

### Identifiers

• HAL Id : hal-02931977, version 1
• ARXIV : 2007.03458

### Citation

Sarah Perrin, Julien Pérolat, Mathieu Laurière, Matthieu Geist, Romuald Elie, et al.. Fictitious Play for Mean Field Games: Continuous Time Analysis and Applications. 2020. ⟨hal-02931977⟩

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