Abstract: The mismatch between the supply of and demand for care services has recently increased pressures on Chinese healthcare systems, fueled by aging populations and scarce high-quality medical resources which is especially concentrated in some 3A hospitals. Our central government has repeatedly emphasized the significance of reallocating high-quality service capacity to some community hospitals to promote the effectiveness and efficiency of the overall healthcare services. However, the problem of interest conflicts between different levels of hospitals pertaining to implementing the high-quality service capacity reallocation program in the hierarchic healthcare systems has not been formally analyzed and addressed. In this paper, three profit-sharing schemes including a Profit-Sharing-for-Capacity (PSC) scheme, Performance Profit-Sharing (PPS) scheme, and Hybrid Profit-Sharing (HPS) scheme are designed, as well as their operating performance for better coordinating the service capacity reallocation is evaluated. By developing a game-theoretic framework with a queueing model, the interactions among the patients, the 3A hospital, and the community hospital are captured. First, all three participants’ equilibrium decisions (patient visit rates, 3A hospital’s service capacity reallocating rate, and community hospital’s profit-reallocation price) and equilibrium outcomes (care accessibility, operating profits, and social welfare) associated with the PSC and PPS schemes are analyzed. Second, the optimum results of the overall centralized healthcare system as compared with those under the two profit-sharing schemes are examined. Finally, the operating performances of the HPS scheme which is a combination of PSC and PPS schemes are investigated. Our findings of studies indicate that when the total high-quality service capacity is sufficiently low, three profit-sharing schemes are equally efficient in accelerating implementing the capacity-reallocation program and improving both care accessibility and social welfare. When the total service capacity is medium, the HPS scheme is always more efficient than the PPS scheme, but only for a relatively low weight parameter of performance sharing in the hybrid scheme, the equilibrium outcomes of the hybrid profit-sharing scheme are closer to the benchmark case associated with the centralized system than those of the PSC scheme. However, when the total service capacity is high enough, the sinking capacity is not beneficial for the overall system and thus reduces social welfare. Through numerical illustration, the operating performances of the three profit-sharing schemes at different levels of high-quality medical resources and the weight parameter of operating profits are further assessed. These useful managerial insights can be readily leveraged by healthcare service providers and regulators to create appropriate policies that are effectively implemented in a high-quality capacity-reallocation program in the hierarchical healthcare delivery system.

Key words: hierarchical healthcare systems； capacity reallocation； coordination scheme；queuing-game theory； social welfare; care accessibility