一种递阶传染病控制的博弈方法
A Game-Theoretic Approach for Hierarchical Epidemic Control
摘要：
我们设计并分析了一个多层次的博弈论模型，该模型涉及疫情控制的分层政策干预，例如应对COVID-19大流行的政策干预。我们的模型捕捉了决策者层次结构中潜在的不匹配的优先级（例如，联邦、州和地方政府），这涉及对政策强度具有相反依赖性的两个成本组成部分-干预后感染率和政策执行的社会经济成本。此外，我们的模型还包括决策中至关重要的第三个因素：不遵守决策者的成本，例如县不遵守州级政策。我们提出了两种新的算法，近似解决方案，这样的游戏。第一种是基于最佳反应动力学（BRD），并利用树结构的游戏。第二个结合了二次整数规划（QIP），这使我们能够崩溃的两个最低水平的游戏，最佳反应动态。通过大量的实验，我们表明，我们的QIP为基础的方法显着优于BRD算法在运行时间和质量的平衡解决方案。最后，我们将基于QIP的算法应用于基于各种参数配置下的合成数据和真实数据的实验，并分析由此产生的（近似）均衡，以深入了解权力下放对整体福利的影响（以成本的负和衡量）以及政策制定者之间成本分配的搭便车和公平性等新兴属性。
英文摘要：
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.
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