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arXiv · 1807.09078

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

Jean-David Benamou·Guillaume Carlier·Simone Di Marino·Luca Nenna
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Abstract

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.

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Jean-David Benamou, Guillaume Carlier, Simone Di Marino, Luca Nenna. 2018-07-24. An entropy minimization approach to second-order variational mean-field games. https://arxiv.org/abs/1807.09078

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