Linear-Quadratic Mean Field Social Optimization with a Major Player
Abstract
This paper considers a linear-quadratic (LQ) mean field control problem involving a major player and a large number of minor players, where the dynamics and costs depend on random parameters. The objective is to optimize a social cost as a weighted sum of the individual costs under decentralized information. We apply the person-by-person optimality principle in team decision theory to the finite population model to construct two limiting variational problems whose solutions, subject to the requirement of consistent mean field approximations, yield a system of forward-backward stochastic differential equations (FBSDEs). We show the existence and uniqueness of a solution to the FBSDEs and obtain decentralized strategies nearly achieving social optimality in the original large but finite population model.
Keywords
Cite
@article{arxiv.1904.03346,
title = {Linear-Quadratic Mean Field Social Optimization with a Major Player},
author = {Minyi Huang and Son Luu Nguyen},
journal= {arXiv preprint arXiv:1904.03346},
year = {2019}
}