5 papers
Semi-Discrete Approximation of Aubry and Mather sets
Fabio Camilli, Cristian Mendico
We study the semi-discrete approximation of Aubry and Mather sets for Tonelli Lagrangians on the flat torus. Starting from the discrete Lax--Oleinik equation, we introduce natural…
A semi-Lagrangian method for solving state constraint Mean Field Games in Macroeconomics
Fabio Camilli, Qing Tang, Yong-shen Zhou
We study continuous-time heterogeneous agent models cast as Mean Field Games, in the Aiyagari-Bewley-Huggett framework. The model couples a Hamilton-Jacobi-Bellman equation for ind…
Li-Yau inequality and related properties on metric star graphs
Fabio Camilli
We prove a Li-Yau gradient estimate for positive solutions to the heat equation defined on a metric star graph $\mG$ given by the heat kernel formula. As consequence, we derive a H…
Stationary Mean Field Games on networks with sticky transition conditions
Jules Berry, Fabio Camilli
We study stochastic Mean Field Games on networks with sticky transition conditions. In this setting, the diffusion process governing the agent's dynamics can spend finite time both…
Learning equilibria in Cournot mean field games of controls
Fabio Camilli, Mathieu Laurière, Qing Tang
We consider Cournot mean field games of controls, a model originally developed for the production of an exhaustible resource by a continuum of producers. We prove uniqueness of the…