Motivated by the problems of imbalance between the supply of and demand for the different levels of hospitals in a hierarchical healthcare system, we propose two contract mechanisms: patient subsidy and capacity investment. Under the patient subsidy scheme, each patient who chooses the primary hospital receives a subsidy from the funder; whereas, under the capacity investment scheme, the primary hospital itself receives investment compensation for expanding service capacity. By employing a game-theoretic queueing model, we determine the optimal decisions (i.e., the patient arrival rate at each hospital, the funder subsidy rate, the primary hospital’s capacity allocation rate, and the funder’s compensation rate) and characterize the equilibrium outcomes (i.e., social welfare, operating profit, patient utility, and waiting time) for both contract mechanisms. We find that the funder’s budget and the size of the patient population play a critical role in scheme performance. The funder must secure a sufficient budget to ensure the effectiveness of either scheme. When the healthcare market is small, the patient subsidy scheme is effective in mitigating the issue of an imbalanced hierarchical system; however, when the market is large and growing, the capacity investment scheme effectively encourages capacity expansion to accommodate the growing demand. Therefore, it is suggested that the funder makes policy decisions based on both the existing and anticipated healthcare system (i.e., market size and development trends), the root issues affecting the system hierarchy, and the associated costs. Additionally, we find that hospital profitability conflicts with total social welfare under some circumstances, and that the funder must therefore strive to align the interests of hospitals with society in order to ensure a successful implementation of the contract scheme
