Equilibrium model for hospital competition with stochastic demands based on government subsidies in a mixed market

By taking medical reform policies into consideration, based on government subsidies and stochastic demands, this paper constructs a stochastic generalized Nash equilibrium model for non-profit and for-profit hospitals. To solve the equilibrium model, we use the Karush-Kuhn-Tucker conditions to reformulate the model into a stochastic mixed complementarity system. Furthermore, the stochastic mixed complementarity system is transformed equivalently into a system of stochastic nonlinear equations, which is solved by some Monte Carlo approximation techniques. The numerical results demonstrate that, in a mixed market, the medical procedures' prices of for-profit hospitals are almost 3 times that of non-profit hospitals, while the quality levels of for-profit hospitals are nearly 50% of non-profit hospitals' quality levels. Competition between non-profit and for-profit hospitals is beneficial for improving the cost control levels of non-profit hospitals. Sensitivity analysis confirms that increasing government subsidy rate does not affect non-profit hospitals' decisions, while cost control levels of for-profit hospitals significantly increase from 1, 000 to 18, 000. Increasing government subsidy rate or taxation rate promotes for-profit hospitals to increase cost control levels and causes no significant impact on non-profit hospitals. Increasing the reimbursement rate of medical insurance is helpful to reduce prices of medical procedures, increase cost control levels, improve medical welfare of patients, and promote orderly competition in a mixed medical market. These results offer valuable insights for effective management of a mixed market.