Linear-Quadratic Mean Field Social Optimization with a Major Player

Minyi Huang; Son Luu Nguyen

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arXiv · 1904.03346

Linear-Quadratic Mean Field Social Optimization with a Major Player

Minyi Huang·Son Luu Nguyen

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Abstract

This paper considers a linear-quadratic (LQ) mean field control problem involving a major player and a large number of minor players, where the dynamics and costs depend on random parameters. The objective is to optimize a social cost as a weighted sum of the individual costs under decentralized information. We apply the person-by-person optimality principle in team decision theory to the finite population model to construct two limiting variational problems whose solutions, subject to the requirement of consistent mean field approximations, yield a system of forward-backward stochastic differential equations (FBSDEs). We show the existence and uniqueness of a solution to the FBSDEs and obtain decentralized strategies nearly achieving social optimality in the original large but finite population model.

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Minyi Huang, Son Luu Nguyen. 2019-04-06. Linear-Quadratic Mean Field Social Optimization with a Major Player. https://arxiv.org/abs/1904.03346

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