A Game-Theoretic Approach for Hierarchical Epidemic Control

Democratic governments and institutions typically have a hierarchical structure. For example, policies in the U.S., Canada, and many European democracies emerge from complex interactions among the federal and state governments, as well as county boards, city councils and mayors. Such interactions are characterized by inherent asymmetries across different levels of the hierarchy. On the one hand, the specifics of policy formulation and enforcement (e.g., training and deployment of personnel and updating of infrastructure) are generally in the hands of administrative bodies at lower levels of the hierarchy -- often the lowest level -- for practical reasons; actions these entities take are the ones that truly matter in the sense that they directly impact costs and benefits realized at all levels. On the other hand, entities at higher levels may have the power to impose constraints in some form or another on the policy-makers within their immediate jurisdiction (e.g., the U.S. federal government can constrain state policies); violations of these constraints, in turn, entail a noncompliance cost to the violator, such as legal costs, penalties, or reputation loss. Examples of such hierarchical policy structure arise in the spheres of education (e.g., topics to be included in primary education), healthcare (e.g., vaccination) and immigration. A preeminent recent example of such hierarchical policy-making is the response to the ongoing COVID-19 pandemic in countries with decentralized administration. Policies concerning social distancing, masking and vaccination have involved recommendations at the federal level, guidelines and restrictions at the state/province/district level, and measures adopted by specific counties, cities or even individual businesses and schools. In general, policies are contentious.