We design and analyze a multi-level game-theoretic model of hierarchical policy interventions for epidemic control, such as those in response to the COVID-19 pandemic. Our model captures the potentially mismatched priorities among a hierarchy of policy-makers (e.g., federal, state, and local governments) with respect to two cost components that have opposite dependence on the policy strength -- post-intervention infection rates and the socio-economic cost of policy implementation. Additionally, our model includes a crucial third factor in decisions: a cost of non-compliance with the policy-maker immediately above in the hierarchy, such as non-compliance of counties with state-level policies. We propose two novel algorithms for approximating solutions to such games. The first is based on best response dynamics (BRD), and exploits the tree structure of the game. The second combines quadratic integer programming (QIP), which enables us to collapse the two lowest levels of the game, with best response dynamics. Through extensive experiments, we show that our QIP-based approach significantly outperforms the BRD algorithm both in running time and the quality of equilibrium solutions. Finally, we apply the QIP-based algorithm to experiments based on both synthetic and real-world data under various parameter configurations and analyze the resulting (approximate) equilibria to gain insight into the impact of decentralization on overall welfare (measured as the negative sum of costs) as well as emergent properties like free-riding and fairness in cost distribution among policy-makers.
翻译:我们设计并分析一个多层次的游戏理论模型,用于控制流行病,例如应对COVID-19流行病的等级政策干预。我们的模型捕捉了决策者(例如联邦、州和地方政府)等级之间在两个成本组成部分方面可能不匹配的优先事项,这两个组成部分对政策实力的依赖正好相反:干预后的感染率和政策执行的社会经济成本。此外,我们的模型包括一个关键的第三个因素:不遵守紧接在等级结构中的决策者的成本,例如各州不遵守州一级政策的情况。我们提出两种新的算法,以接近这种游戏的解决办法。第一个是建立在最佳反应动态(BRD)基础上的,利用游戏的树结构。第二个组合是四重整编程(QIP),这使我们能够打破游戏的两层最低层次,产生最佳的反应动态。我们通过广泛的实验,显示我们基于QIP的方法大大优于BRD的算法,既在时间运行中,又在平衡解决方案的质量上,我们提出了两种新的算法。最后,我们把基于最佳反应动力的货币结构的货币结构,也就是根据各种货币结构的货币结构,将各种货币结构的货币结构分析结果,作为基础的货币结构的货币结构分析,作为根据实际的货币结构的货币结构分析。