Joint optimal strategies on service investment and drug pricing for a two-sided online pharmaceutical platform

We study a monopoly pharmaceutical platform that acts as a two-sided market provider and an e-tailer simultaneously. The platform, on which physicians participate after paying an entrance fee, links physicians and patients through the diagnosis service provided by physicians. Patients can also buy prescription drugs sold by the platform. The platform conducts service investment to attract patients and maximizes its profit by setting an appropriate entrance fee and drug price. We deal with the optimization problem under different conditions, which may be either convex or non-convex. We find that, in general, the platform can achieve its maximized profit when it reduces drug prices to stimulate more patients to buy drugs after being diagnosed. Besides, service investment plays different roles in attracting patients as the disease severity varies. When the disease is less severe, the improvement of service investment mainly increases the number of patients who choose to be diagnosed on the platform. However, when the disease is severer, a more significant service investment can induce patients to purchase drugs. Furthermore, it is more beneficial for the platform to charge physicians for an entry fee rather than sharing the drug revenue with them.