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arXiv · 2007.12830

Social Optima in Leader-Follower Mean Field Linear Quadratic Control

Jianhui Huang·Bing-Chang Wang·Tinghan Xie
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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.

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Jianhui Huang, Bing-Chang Wang, Tinghan Xie. 2020-07-25. Social Optima in Leader-Follower Mean Field Linear Quadratic Control. https://arxiv.org/abs/2007.12830

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