This paper investigates the linear-quadratic social control problem for mean field systems with unmodeled dynamics and multiplicative noise. The objective of each agent is to optimize the social cost in the worst-case disturbance. We first analyze the centralized strategies by the person-by-person optimality and then construct an auxiliary zero-sum game according to mean field approximations. By solving the auxiliary problem subject to consistency conditions, we design a set of decentralized strategies, which is further shown to have asymptotic robust social optimality.

中文翻译：

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具有未建模动力学和乘法噪声的线性二次平均场控制中的社会最优解

本文研究了具有未建模动力学和乘法噪声的平均场系统的线性二次社会控制问题。每个代理的目标是在最坏情况下优化社会成本。我们首先通过逐人优化分析集中策略，然后根据平均场近似构造辅助零和博弈。通过解决一致性条件下的辅助问题，我们设计了一套分散的策略，进一步证明了它具有渐近鲁棒的社会最优性。