A Dynamic Game Analysis of Hospitals’ Quality-Improving and Congestion-Reducing with Corresponding Knowledge Accumulations Effects

In this paper, we develop a dynamic control to investigate the hospitals’ quality improvement and congestion reduction, along with corresponding knowledge accumulations. The main features of our work are: (i) developing a dynamic analysis model of the hospitals’ quality improvement and congestion reduction, considering knowledge accumulations in health care markets; (ii) the demand function for medical treatment depends on treatment quality, congestion degree, price, and traveling cost; (iii) each hospital’s instantaneous costs of quality improvement and congestion reduction depend on treatment quality, quality-improving investment, corresponding knowledge accumulation as well as congestion degree, congestion-reducing investment and the corresponding knowledge accumulation; (iv) the hospitals’ dynamic competitions are not only in treatment quality and congestion degree but also in treatment prices. Our results show that (i) there exists a unique saddle-stable steady-state equilibrium under hospital optimum and social optimum; (ii) knowledge accumulation and the complementarity or substitutability affect the hospitals’ decision behavior; (iii) whether the price and the hospitals’ investments in quality improvement and congestion reduction are higher or lower under hospital optimum than that under social optimum depends on the parameter regions of complementarity or substitutability.