Joint optimization of service investment and pricing strategy in an online pharmaceutical platform with fairness concern
摘要
We study a monopoly online pharmaceutical two-sided platform with two types of users, physicians and patients. Physicians utilize the platform to provide diagnostic service to patients, while the platform provides medicine sales and value-added services to patients. We consider two pricing schemes for physicians to join the platform, including the fixed and linear pricing scheme. We deal with the joint optimization problem of value-added service investment and retail price of medicine under the two pricing schemes for physicians with fairness concern, and derive the optimal equilibrium solutions. By comparing optimal equilibrium solutions and fairness-adjusted utility under two schemes, we provide scientific strategies for pharmaceutical platforms to choose pricing schemes. In addition, we analyze the effects of marginal investment cost, physician and patient market size on service investment quantity and retail price of medicine. The results show following conclusions: under the fixed pricing scheme, fixed settlement fee is simply correlated with patient market size, but the correlation with physician market size also depends on the patient’s initial utility; under the linear pricing scheme, the diagnostic revenue share ratio affects the optimal service investment and retail price of medicine. Furthermore, our study shows that fairness concern have no impact on the optimal solution in the fixed pricing scheme. Conversely, the optimal solution under the linear pricing scheme is affected by fairness concern, especially when the patient’s initial utility is low.