发表机构
University of Illinois Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出基于预算约束的Stackelberg均值场博弈模型，研究政府如何通过社交距离和疫苗接种策略控制流行病，并给出均衡存在性、唯一性及数值求解算法。
AI 中文摘要
流行病缓解在实践中是有代价的，当预算有限时，其有效分配成为公共政策中的一个重要问题。本文通过Stackelberg均值场博弈研究流行病控制，其中代表政府的领导者（principal）在预算支出过程约束下，为大量理性的小个体（minor agents）选择社交距离指南和疫苗接种水平。领导者预见到小个体的均值场纳什均衡（MFNE），并选择干预策略以最小化自身目标，从而引出一个双层最优控制问题。我们定义了Stackelberg均值场博弈均衡（SMFE），并通过前向-后向常微分方程（FBODE）系统给出了其必要条件，同时提供了存在性和唯一性结果。我们进一步提出一种迭代不动点算法来数值求解FBODE，并展示计算结果以说明由此产生的均衡行为。
英文摘要
Epidemic mitigation comes with a price in practice, and when budget is limited, its effective allocation becomes an important question on public policy. In this paper, we study epidemic control through a Stackelberg mean-field game in which a principal, representing the government, chooses social distancing guidelines and vaccination levels for a large population of rational minor agents subject to a budget-spending process. The principal anticipates the minor agents mean-field Nash equilibrium (MFNE) and selects intervention policies to minimize her own objective, inducing a bi-level optimal control problem. We define the Stackelberg mean-field game equilibrium (SMFE) and give its necessary condition by a forward-backward ordinary differential equation (FBODE) system, and provide existence and uniqueness results. We further propose an iterative fixed-point algorithm to solve the FBODE numerically and present computational observations that illustrate the resulting equilibrium behavior.
CommentsAccepted at 65th IEEE Conference on Decision and Control (CDC 2026)
