We present the design and analysis of a multi-level game-theoretic model of hierarchical policy-making, inspired by policy responses 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 main cost components that have opposite dependence on the policy strength, such as post-intervention infection rates and the cost of policy implementation. Our model further 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 state with federal policies. Our first contribution is a closed-form approximation of a recently published agent-based model to compute the number of infections for any implemented policy. Second, we present a novel equilibrium selection criterion that addresses common issues with equilibrium multiplicity in our setting. Third, we propose a hierarchical algorithm based on best response dynamics for computing an approximate equilibrium of the hierarchical policy-making game consistent with our solution concept. Finally, we present an empirical investigation of equilibrium policy strategies in this game in terms of the extent of free riding as well as fairness in the distribution of costs depending on game parameters such as the degree of centralization and disagreements about policy priorities among the agents.

中文翻译：

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分层政策制定的博弈论方法

我们根据对COVID-19大流行的政策回应，提出了分层决策的多层次博弈论模型的设计和分析。我们的模型捕获了决策者层次结构（例如联邦，州和地方政府）中与两个主要成本成分之间潜在不匹配的优先级，而这两个主要成本成分对策略强度的依赖程度相反，例如干预后的感染率和政策执行成本。我们的模型还包括决策中的第三个关键因素：不遵守上级决策者的成本，例如州不遵守联邦政策。我们的第一项贡献是对最近发布的基于代理的模型进行闭式近似，以计算任何已实施策略的感染数量。第二，我们提出了一种新颖的平衡选择准则，该准则解决了我们环境中具有平衡多重性的常见问题。第三，我们提出了一种基于最佳响应动力学的层次算法，用于计算与我们的解决方案概念一致的层次决策游戏的近似平衡。最后，我们根据搭便车的程度以及费用分配的公平性，对这场博弈中的均衡政策策略进行了实证研究，这取决于博弈参数，例如集中程度和代理商之间政策优先级的分歧。我们提出了一种基于最佳响应动力学的分层算法，用于计算与我们的解决方案概念一致的分层决策博弈的近似均衡。最后，我们根据搭便车的程度以及费用分配的公平性，对这场博弈中的均衡政策策略进行了实证研究，这取决于博弈参数，例如集中程度和代理商之间政策优先级的分歧。我们提出了一种基于最佳响应动力学的分层算法，用于计算与我们的解决方案概念一致的分层决策博弈的近似均衡。最后，我们根据搭便车的程度以及费用分配的公平性，对这场博弈中的均衡政策策略进行了实证研究，这取决于博弈参数，例如集中程度和代理商之间政策优先级的分歧。