Section: New Results
An entropy minimization approach to second-order variational mean-field games
J-D. Benamou, G. Carlier, S. Di Marino, L. Nenna
In [26] 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.