An entropy minimization approach to second-order variational mean-field games
Provides a new theoretical perspective and practical algorithm for solving mean-field games, which are important in economics and multi-agent systems.
The paper establishes an equivalence between variational mean-field games with diffusion and quadratic Hamiltonian and a relative entropy minimization problem, enabling an efficient algorithm based on the Sinkhorn scaling algorithm with Γ-convergence guarantees as the time step vanishes.
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 $Γ$-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.