Master Equation for Cournot Mean Field Games of Control with Absorption
Analysis of PDEs
2022-08-25 v2 Optimization and Control
Abstract
We establish the existence and uniqueness of a solution to the master equation for a mean field game of controls with absorption. The mean field game arises as a continuum limit of a dynamic game of exhaustible resources modeling Cournot competition between producers. The proof relies on an analysis of a forward-backward system of nonlocal Hamilton-Jacobi/Fokker-Planck equations with Dirichlet boundary conditions. In particular, we establish new a priori estimates to prove that solutions are differentiable with respect to the initial measure.
Keywords
Cite
@article{arxiv.2111.07020,
title = {Master Equation for Cournot Mean Field Games of Control with Absorption},
author = {P. Jameson Graber and Ronnie Sircar},
journal= {arXiv preprint arXiv:2111.07020},
year = {2022}
}