{"ID":2833364,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2512.03535","arxiv_id":"2512.03535","title":"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.","short_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 def...","url_abs":"https://arxiv.org/abs/2512.03535","url_pdf":"https://arxiv.org/pdf/2512.03535v1","authors":"[\"Bing-Chang Wang\",\"Huanshui Zhang\",\"Ji-Feng Zhang\"]","published":"2025-12-03T07:55:02Z","proceeding":"math.OC","tasks":"[\"math.OC\"]","methods":"[]","has_code":false}