Pricing and prioritization in a duopoly with self-selecting, heterogeneous, time-sensitive customers under low utilization

Abstract

Time is often used as a differentiating factor in several service operations contexts by service providers (SPs) who prioritize their customers. We use a three-stage game to investigate the competition between two SPs providing service with relatively low utilization to impatient and patient customers. In the first stage, the SPs decide whether to offer single service in which customers are seen on a first-come-first-serve basis or differentiated service with prioritization. In the second stage, they set their prices. In the third stage, customers self-select and make their purchase decisions. We use a novel approach to model customers’ self-selection through an optimization problem with appropriate individual rationality (IR) and incentive compatibility (IC) conditions. In the pricing subgame, we focus on scenarios in which all customers get a positive net utility from using the service. 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 determine the overall equilibrium. We derive conditions (on customer heterogeneity and the fraction of impatient customers) for SS, SD, or DD to result in the overall equilibrium.