Pricing and Prioritization in a Duopoly with Self-Selecting, Heterogeneous, Time-Sensitive Customers under Low Utilization

Time is often used as a differentiating factor in several service operations contexts by service providers (SPs) who prioritize their customers. We investigate the competition between two SPs involving a three-stage game. In the first stage, the SPs decide whether single service, in which customers are not prioritized, or differentiated service, with two service classes, should be offered. In the second stage, they set their prices. In the third stage, customers self-select and decide which option they should purchase. There are two types of time-sensitive customers, impatient and patient, with different delay sensitivities. We use a novel approach to model customers' self-selection through an optimization problem with appropriate individual rationality (IR) and incentive compatibility (IC) conditions. We analyze the following three kinds of service delivery by the SPs, and we characterize different types of equilibrium associated with them: (i) SS in which both SPs provide single service, (ii) SD in which one SP provides single service and the other SP provides differentiated service, and (iii) DD in which both of them provide differentiated service. We then use these results to obtain the overall equilibrium under different numerical examples. We derive conditions (on customer heterogeneity and the fraction of impatient customers) for SS, SD, or DD to result in the overall equilibrium