arXiv subjects

Marco Masoero

Publications and source records attributed to Marco Masoero.

3 recordsLinked to original sources

arXiv2019

Weak KAM theory for potential MFG

We develop the counterpart of weak KAM theory for potential mean field games. This allows to describe the long time behavior of time-dependent potential mean field game systems. Our main result is the existence of a limit, as time tends to infinity, of the value function of an optimal control problem stated in the space of measures. In addition, we show a mean field limit for the ergodic constant associated with the corresponding Hamilton-Jacobi equation.

math.AP↗

arXiv2019

Convergence of the solutions of the MFG discounted Hamilton-Jacobi equation

We consider the solution $\mathcal V_δ$ of the discounted Hamilton-Jacobi equation in the Wasserstein space arising from potential MFG and we prove its full convergence to a corrector function $χ_0$. We follow the structure of the proof of the analogue result in the finite dimensional setting provided by Davini, Fathi, Iturriaga, Zavidovique in 2017. We characterize the limit $χ_0$ through a particular set of smooth Mather measures. A major point that distinguishes the techniques deployed in the standard setting from the ones that we use here is the lack of mollification in the Wasserstain space.

math.AP↗

arXiv2018

On the long time convergence of potential MFG

We look at the long time behavior of potential Mean Field Games (briefly MFG) using some standard tools from weak KAM theory. We first show that the time-dependent minimization problem converges to an ergodic constant $-λ$, then we provide a class of examples where the value of the stationary MFG minimization problem is strictly greater than $-λ$. This will imply that the trajectories of the time-dependent MFG system do not converge to static equilibria.

math.OC↗