English

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}
}