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arXiv · 2012.15468

Linear quadratic mean field social optimization: Asymptotic solvability and decentralized control

Minyi Huang·Xuwei Yang
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Abstract

This paper studies asymptotic solvability of a linear quadratic (LQ) mean field social optimization problem with controlled diffusions and indefinite state and control weights. Starting with an $N$-agent model, we employ a rescaling approach to derive a low-dimensional Riccati ordinary differential equation (ODE) system, which characterizes a necessary and sufficient condition for asymptotic solvability. The decentralized control obtained from the mean field limit ensures a bounded optimality loss in minimizing the social cost having magnitude $O(N)$, which implies an optimality loss of $O(1/N)$ per agent. We further quantify the efficiency gain of the social optimum with respect to the solution of the mean field game.

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Minyi Huang, Xuwei Yang. 2020-12-31. Linear quadratic mean field social optimization: Asymptotic solvability and decentralized control. https://arxiv.org/abs/2012.15468

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