Calculus of Variations and Geometric Measure Theory

J. D. Benamou - G. Carlier - S. Di Marino - L. Nenna

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

created by dimarino on 24 Jul 2018
modified by nenna on 01 Apr 2019


Accepted Paper

Inserted: 24 jul 2018
Last Updated: 1 apr 2019

Journal: M3AS
Year: 2018


We propose a new viewpoint on variational mean-field games with diffusion and quadratic Hamiltonian. We show the equivalence of such mean-field games with a relative entropy minimization at the level of probabilities on curves. We also address the time-discretization of such problems, establish $\Gamma$-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.