A Game-Theoretic Approach for Hierarchical Epidemic Control

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.