Coordination schemes for resource reallocation and patient transfer in hospital alliance models

In many countries, healthcare systems encounter the issue of imbalance between supply and demand in a hierarchical structure. The comprehensive hospitals, which possess more high-quality resources, are often overwhelmed, while their counterparts, community hospitals, are often idle. To address this imbalance issue, certain payment schemes are generally considered effective in motivating comprehensive hospitals to divert patients downstream via resource transfer. In addition to two particular payment schemes, namely, patient payment (PP) and fee-for-capacity (FFC), this study also considers two hospital alliance models, the government-led (GL-type) and the hospital-forged (HF-type) alliance, for effectively overcoming the imbalance issue. Compared to the HF-type alliance, in which each community hospital determines the price paid to the comprehensive hospital for transferring resources, the GL-type alliance requires the payment price to be set by the regulator. Methodologically, this study devises a three-stage sequential game to characterize the dynamics among the various entities, such as the regulator, the comprehensive hospital, the community hospitals, and the patients. Equilibrium results, in terms of the capacity sinking rate and patient transfer rate, are derived, and scheme and alliance performances are evaluated using various measurements, such as patient utility, and hospital and social welfare. We find that a direct payment scheme (FFC) under a centralized alliance model (GL-type alliance) is more effective for both making decisions (about the patient transfer rate, capacity sinking rate, and payment price) and the performances (of each hospital's welfare, patient welfare, the waiting time per patient, and social welfare). Furthermore, our study examines the impacts of the alliance scale and finds that social welfare is first decreasing and then increasing with alliance scale. Therefore, it is suggested to establish either a one-to-one hospital alliance (consisting of a comprehensive and a community hospital) or a large-scale (e.g., a comprehensive and 10 community hospitals) hospital alliance.