Paid Priority in Service Systems: Theory and Experiments

Abstract

Problem definition: Motivated by the prevalence of paid priority programs in practice, we study a service provider operating a system in which customers have random waiting costs and choose between two queues: regular (no cost) or priority (for a fee). We also consider a mechanism by which the provider redistributes a portion of priority revenue to compensate regular-queue customers for their longer waits. Methodology/results: To determine the waiting-cost-dependent equilibrium priority purchasing strategies, we establish structural results at a sample-path level and prove that they generalize. In models both with and without compensation, the equilibrium exhibits a cost-dependent, increasing-threshold structure. We also prove that compensation entails fewer priority purchases because compensating regular-queue customers makes priority less attractive. We then analyze system-wide performance. Despite the fewer priority purchases, for a fixed (low) priority fee, compensation can actually reduce equilibrium aggregate waiting cost by filtering low-waiting-cost customers out of the priority queue; however, this finding does not hold when comparing at the optimal fees. We then test our models in the laboratory. Key behavioral regularities are that low-cost subjects are overrepresented (underrepresented) in the priority (regular) queue compared with equilibrium, and subjects with low and high waiting costs tend to overbuy priority at high fees. Managerial implications: Our theoretical and behavioral results guide service providers in managing priority service systems. First, we find that compensation does not provide short-term performance benefits. Second, our experiments reveal that suboptimal customer decisions partially prevent efficient reordering of customers by waiting cost, leading to higher aggregate waiting cost than the equilibrium predicts, but still lower than under first-come, first-serve service. Finally, because customers tolerate higher fees than they should, a revenue-maximizing provider can set a higher priority fee and extract more revenue than it could if customers acted rationally. Funding: This work was supported by the Center and Laboratory for Behavioral Operations and Economics at the Naveen Jindal School of Management at The University of Texas at Dallas. Supplemental Material: The online appendix is available at https://doi.org/10.1287/msom.2021.0387 .