Hierarchical Governance in Public Crisis: A Differential Game Analysis of Epidemic Containment, Economic Stability, and Transition Timing

In the complex scenario of a major epidemic, apart from the superior government's efforts to promote policy implementation through political incentives and fiscal transfer payments, local governments must strive to balance the inherent tension between public health containment policies and economic stability objectives. In addition, they must carefully select the appropriate transition timing from the emergency response phase to the routine management phase. Considering the hierarchical governance structure and the strategic dynamic decision-making processes involved, this paper examines the equilibrium decision-makings of resource allocation and transition timing between superior and local governments within a differential game framework. Our analysis reveals that during the emergency stage, amplifying political incentives and subsidizing localized epidemic prevention costs robustly enhance policy implementation efficiency. Conversely, in the routine management phase, increased fiscal support for epidemic control exhibits diminishing returns, as effectiveness becomes contingent on the prioritization of economic recovery over sustained containment. Furthermore, the optimal transition timing between two phases depends critically on the marginal cost of containment policies and regional economic growth rates. Methodologically, this study develops a dynamic public crisis management framework that integrates fiscal mechanisms with political incentive structures, offering policymakers a quantitative instrument for designing multi-level and multi-stage governance strategies. The findings not only enhance the flexibility of the pandemic response systems but also provide a theoretical foundation for analyzing the dynamic implementation of policies in the hierarchical governance.