Social Optima in Leader-Follower Mean Field Linear Quadratic Control
Abstract
This paper investigates a linear quadratic mean field leader-follower team problem, where the model involves one leader and a large number of weakly-coupled interactive followers. The leader and the followers cooperate to optimize the social cost. Specifically, for any strategy provided first by the leader, the followers would like to choose a strategy to minimize social cost functional. Using variational analysis and person-by-person optimality, we construct two auxiliary control problems. By solving sequentially the auxiliary control problems with consistent mean field approximations, we can obtain a set of decentralized social optimality strategy with help of a class of forward-backward consistency systems. The relevant Stackelberg equilibrium is further proved under some proper conditions.
Keywords
Cite
@article{arxiv.2007.12830,
title = {Social Optima in Leader-Follower Mean Field Linear Quadratic Control},
author = {Jianhui Huang and Bing-Chang Wang and Tinghan Xie},
journal= {arXiv preprint arXiv:2007.12830},
year = {2020}
}