Invite Your Friend and You’ll Move Up in Line: Optimal Design of Referral Priority Programs

Abstract

This paper studies the optimal design of referral priority programs, in which customers on a waitlist can jump the line by inviting their friends to also join the waitlist. Recent years have witnessed a growing presence of referral priority programs as a novel customer acquisition strategy for firms that maintain a waitlist. Different variations of this scheme are seen in practice, raising the question of what should be the optimal referral priority mechanism. We build an analytical model that integrates queueing theory into a mechanism design framework, where the objective of the firm is to maximize the system throughput, i.e., to accelerate customer acquisition as much as possible. Our analysis shows that the optimal mechanism has one of the following structures: full-priority, partial priority, first-in-first-out (FIFO), and strategic delay. A full-priority (partial-priority) scheme enables referring customers to get ahead of all (only some) non-referring ones. A FIFO scheme does not provide any priority-based referral incentive. A strategic-delay scheme grants full priority to referring customers, but artificially inflates the delay of non-referring ones. We show that FIFO is optimal if either the base market size or the referral cost is large. Otherwise, partial priority is optimal if the base market size is above a certain threshold; full priority is optimal at the threshold base market size; strategic delay is optimal if the base market size is below the threshold. We also find that referrals motivate the firm to maintain a larger capacity and therefore, can surprisingly shorten the average delay even though more customers sign up and strategic delay is sometimes inserted. Our paper provides prescriptive guidance for launching the optimal referral priority program and rationalizes common referral schemes seen in practice.