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Discrete potential mean field games

Frédéric Bonnans 1 Pierre Lavigne 1 Laurent Pfeiffer 1
1 COMMANDS - Controle, Optimisation, modèles, Méthodes et Applications pour les Systèmes Dynamiques non linéaires
CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique, Inria Saclay - Ile de France
Abstract : We propose and investigate a general class of discrete time and finite state space mean field game (MFG) problems with potential structure. Our model incorporates interactions through a congestion term and a price variable. It also allows hard constraints on the distribution of the agents. We analyze the connection between the MFG problem and two optimal control problems in duality. We present two families of numerical methods and detail their implementation: (i) primal-dual proximal methods (and their extension with nonlinear proximity operators), (ii) the alternating direction method of multipliers (ADMM) and a variant called ADM-G. We give some convergence results. Numerical results are provided for two examples with hard constraints.
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Preprints, Working Papers, ...
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https://hal.inria.fr/hal-03260057
Contributor : Pierre Lavigne <>
Submitted on : Tuesday, June 15, 2021 - 11:34:39 AM
Last modification on : Friday, June 18, 2021 - 3:42:03 AM

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Potential-Numerics-MFG.pdf
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  • HAL Id : hal-03260057, version 2

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Frédéric Bonnans, Pierre Lavigne, Laurent Pfeiffer. Discrete potential mean field games. 2021. ⟨hal-03260057v2⟩

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