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arXiv · 2512.03535

Leader-Follower Mean Field LQG Games with Multiplicative Noise

Bing-Chang Wang·Huanshui Zhang·Ji-Feng Zhang
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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.

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Bing-Chang Wang, Huanshui Zhang, Ji-Feng Zhang. 2025-12-03. Leader-Follower Mean Field LQG Games with Multiplicative Noise. https://arxiv.org/abs/2512.03535

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