Equilibrium model for hospital competition based on patient choices and government subsidies

In order to study the competition strategies of medical institutions under market mechanism and government supervision, taking the current medical policies into consideration, we establish a nonconvex generalized Nash equilibrium model with upper bounds for demands of regional medical procedures based on patient choices and government subsidies. By introducing some auxiliary variables to deal with the fractional objective functions, we make use of the block coordinate descent method to decompose the nonconvex optimization problem into two convex subproblems and then use their Karush-Kuhn-Tucker conditions to transform them into a mixed complementarity system. Furthermore, to test the effectiveness of the considered model, we employ Python 3.7.3 to give some numerical experiments and the sensitivity analysis of the government subsidies and the hospital altruistic behaviors. The numerical results indicate that, with the increase of government subsidies, the prices of medical procedures together with marginal utility decrease gradually, whereas the quality of medical procedures, the level of cost control, and the total benefits increase accordingly. This reveals that increasing total government subsidies modestly can alleviate the difficulties caused by patients' seeking treatment and hospital operational management. In addition, when the altruism is introduced, the operational efficiency of hospitals increases to some extent, which means that establishing and improving regulatory system of hospital altruism is helpful in increasing economic benefits and promoting sustainable development in the medical markets. © 2021, Editorial Board of Journal of Systems Engineering Society of China. All right reserved.