A Class of Infinite Horizon Mean Field Games on Networks
Analysis of PDEs
2018-05-30 v1
Abstract
We consider stochastic mean field games for which the state space is a network. In the ergodic case, they are described by a system coupling a Hamilton-Jacobi-Bellman equation and a Fokker-Planck equation, whose unknowns are the invariant measure m, a value function u, and the ergodic constant . The function u is continuous and satisfies general Kirchhoff conditions at the vertices. The invariant measure m satisfies dual transmission conditions: in particular, m is discontinuous across the vertices in general, and the values of m on each side of the vertices satisfy special compatibility conditions. Existence and uniqueness are proven, under suitable assumptions.
Keywords
Cite
@article{arxiv.1805.11290,
title = {A Class of Infinite Horizon Mean Field Games on Networks},
author = {Yves Achdou and Manh-Khang Dao and Olivier Ley and Nicoletta Tchou},
journal= {arXiv preprint arXiv:1805.11290},
year = {2018}
}