Weak solutions of the master equation for Mean Field Games with no idiosyncratic noise
Analysis of PDEs
2021-10-01 v1
Abstract
We introduce a notion of weak solution of the master equation without idiosyncratic noise in Mean Field Game theory and establish its existence, uniqueness up to a constant and consistency with classical solutions when it is smooth. We work in a monotone setting and rely on Lions' Hilbert space approach. For the first-order master equation without idiosyncratic noise, we also give an equivalent definition in the space of measures and establish the well-posedness.
Keywords
Cite
@article{arxiv.2109.14911,
title = {Weak solutions of the master equation for Mean Field Games with no idiosyncratic noise},
author = {Pierre Cardaliaguet and Panagiotis Souganidis},
journal= {arXiv preprint arXiv:2109.14911},
year = {2021}
}