Leader-Follower Mean Field LQG Games with Multiplicative Noise
Abstract
This paper studies open-loop and feedback solutions to leader-follower mean field linear-quadratic-Gaussian games with multiplicative noise by the direct approach. The leader-follower game involves a leader and many followers, where the state and control weight matrices in their costs are not limited to be positive definite. From variational analysis with mean field approximations, we obtain a set of open-loop controls in terms of solutions to mean field forward-backward stochastic differential equations. By applying the matrix maximum principle, a set of decentralized feedback strategies is constructed. Distinct from traditional works, a cross term has appeared in derivation due to the presence of mean field terms. For open-loop and feedback solutions, the corresponding optimal costs of all players are explicitly given in terms of the solutions to two Riccati equations, respectively.
Keywords
Cite
@article{arxiv.2512.03535,
title = {Leader-Follower Mean Field LQG Games with Multiplicative Noise},
author = {Bing-Chang Wang and Huanshui Zhang and Ji-Feng Zhang},
journal= {arXiv preprint arXiv:2512.03535},
year = {2025}
}