Optimal and incentive compatible pricing for heterogeneous periods

Abstract

This paper studies a service firm whose business time can be divided into several periods, each providing different value to customers. Heterogeneous service is a major reason resulting in imbalances between supply and demand. Since customers differ in their degree of impatience, firms can use differential pricing mechanisms to optimize their objectives and match supply with demand in each period, by inducing customers to choose different periods. We study two types of firms, an internal firm, the objective of which is to maximize the system’s (including the firm and all the customers) total net value, and a commercial firm, which aims to optimize its own profit. Though impatience factors are customers’ private information, for each type of firm, we derive the optimal incentive compatible pricing policy, under which all the coming customers will follow the firm’s assignment, that is, patient customers will buy the service in high-value periods, but their waiting time will be longer, while impatient customers will enter into the low-value periods, but they will be compensated by shorter waiting times. Furthermore, in the internal firm, we also prove that this mechanism enables the decentralization of decisions, while maintaining centralized system-wide optimality. Numerical analysis shows that when there is sufficient capacity, the internal firm does not always need to set lower prices than the commercial firm in every period.

Keywords

Delay cost / queuing / differential pricing / information asymmetry / incentive compatibility

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