8 papers
A Fully Discrete Variational Approximation of Mather Measures and Sets
Fabio Camilli, Cristian Mendico
We introduce a fully--discrete variational approximation of Mather measures and sets for Tonelli Lagrangians on the flat torus, together with a numerical procedure for approximatin…
Semi-discrete approximation of Mañé, Aubry and Mather sets
Fabio Camilli, Cristian Mendico
We study a variational discretization in time of Aubry--Mather theory for Tonelli Lagrangians on the flat torus. We define discrete Mañé, Aubry and Mather sets, establish their com…
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…
A note on first order quasi-stationary Mean Field Games
Fabio Camilli, Claudio Marchi, Cristian Mendico
Quasi-stationary Mean Field Games models consider agents who base their strategies on current information without forecasting future states. In this paper we address the first-orde…
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…
On the quadratic convergence of Newton's method for Mean Field Games with non-separable Hamiltonian
Fabio Camilli, Qing Tang
We analyze asymptotic convergence properties of Newton's method for a class of evolutive Mean Field Games systems with non-separable Hamiltonian arising in mean field type models w…