HAL will be down for maintenance from Friday, June 10 at 4pm through Monday, June 13 at 9am. More information
Skip to Main content Skip to Navigation
Preprints, Working Papers, ...

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

Sarah Perrin 1 Julien Pérolat 2, 1 Mathieu Laurière 3 Matthieu Geist 4 Romuald Elie 5 Olivier Pietquin 6
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.
Complete list of metadata

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 : Thursday, March 24, 2022 - 3:43:48 AM

Links full text

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⟩

Share

Metrics

Record views

87