An entropy minimization approach to second-order variational mean-field games-Reference-Cited by-同舟云学术

An entropy minimization approach to second-order variational mean-field games

Published:2019-07 Issue:08 Volume:29 Page:1553-1583
ISSN:0218-2025
Container-title:Mathematical Models and Methods in Applied Sciences
language:en
Short-container-title:Math. Models Methods Appl. Sci.

Author:

Benamou Jean-David¹²,Carlier Guillaume¹²,Di Marino Simone³,Nenna Luca⁴

Affiliation:

1. INRIA-Paris, MOKAPLAN, rue Simone Iff, 75012 Paris, France

2. CEREMADE, UMR CNRS 7534, PSL Université Paris Dauphine, Pl. de Lattre de Tassigny, 75775 Paris Cedex 16, France

3. Indam, Unità SNS, Pisa, Italy

4. Laboratoire de Mathématiques d’Orsay, Univ. Paris-Sud, CNRS, Université Paris-Saclay, 91405 Orsay, France

Abstract

We propose an entropy minimization viewpoint on variational mean-field games with diffusion and quadratic Hamiltonian. We carefully analyze the time discretization of such problems, establish [Formula: see text]-convergence results as the time step vanishes and propose an efficient algorithm relying on this entropic interpretation as well as on the Sinkhorn scaling algorithm.

Publisher

World Scientific Pub Co Pte Lt

Subject

Applied Mathematics,Modelling and Simulation

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0218202519500283

Reference35 articles.

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4. L. Ambrosio, N. Fusco and D. Pallara, Functions of Bounded Variation and Free Discontinuity Problems, Oxford Mathematical Monographs (The Clarendon Press, Oxford Univ. Press, 2000), 434 pp.

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