Search Among Queues Under Quality Differentiation

Abstract

Customers looking for service providers often face search frictions and have to trade off quality and availability. To understand customers' search behavior when they are confronted with a large collection of vertically differentiated, congested service providers, we build a model in which arriving customers conduct costly sequential search to resolve uncertainty about service providers' quality and queue length and select one to join by optimal stopping rules. Customers search due, in part, to variations in waiting time across service providers, which, in turn, are determined by the search behavior of customers. Thus, an equilibrium emerges. We characterize customers' equilibrium search/join behavior in a mean field model as the number of service providers grows large. We find that reducing either the search cost or customer arrival rate may increase the average waiting time in the system as customers substitute toward high quality service providers. Moreover, with lower search costs, the improved quality obtained by customers may not make up for the prolonged wait, therefore degrading the average search reward, and, more importantly, decreasing customer welfare; when customers search, their welfare can even be lower than if they are not allowed to search at all.

Keywords: queuing games, search, waiting time, quality substitution, customer welfare