Mean Field Game with Delay: a Toy Model
Probability
2018-08-21 v2
Abstract
We study a toy model of linear-quadratic mean field game with delay. We "lift" the delayed dynamic into an infinite dimensional space, and recast the mean field game system which is made of a forward Kolmogorov equation and a backward Hamilton-Jacobi-Bellman equation. We identify the corresponding master equation. A solution to this master equation is computed, and we show that it provides an approximation to a Nash equilibrium of the finite player game.
Keywords
Cite
@article{arxiv.1807.04795,
title = {Mean Field Game with Delay: a Toy Model},
author = {Jean-Pierre Fouque and Zhaoyu Zhang},
journal= {arXiv preprint arXiv:1807.04795},
year = {2018}
}