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

Problem definition : This paper studies the optimal design of referral priority programs, in which customers on a waiting list can jump the line by inviting their friends to also join the waiting list. Academic/practical relevance : Recent years have witnessed a growing presence of referral priority programs as a novel customer-acquisition strategy for firms that maintain a waiting list. Different variations of this scheme are seen in practice, raising the question of what should be the optimal referral priority mechanism. Methodology : I build an analytical model that integrates queuing theory into a mechanism design framework in which the objective of the firm is to maximize the system throughput, that is, accelerate customer acquisition as much as possible. Results : My 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) nonreferring 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 nonreferring ones. I 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. I 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. Managerial implications : My paper provides prescriptive guidance for launching an optimal referral priority program and rationalizes common referral schemes seen in practice.