Optimal Mechanism Design with Referral

Abstract

This paper establishes the optimal selling mechanism when a seller can incentivize an existing buyer to refer his privately known potential buyer to participate. We identify three optimal channels for providing referral incentives. First, if the existing buyer declares that no potential buyer exists, his virtual value is penalized. Second, if the existing buyer refers the potential buyer to the seller, his virtual value is boosted. Third, in some scenarios where this carrots-and-sticks-via-virtual-value approach is insufficient for creating proper referral incentives, the existing buyer is then given a constant referral bonus for referring the potential buyer. We also provide conditions under which the optimal mechanism can be implemented using simple mechanisms. Finally, we demonstrate that the conventional resale mechanism is suboptimal. This paper was accepted by Itai Ashlagi, revenue management and market analytics. Funding: H. Zhou’s research is supported by the Chenguang Program of Shanghai Education Development Foundation and Shanghai Municipal Education Commission [Grant 22CGA77]. Supplemental Material: The online appendix is available at https://doi.org/10.1287/mnsc.2023.01540 .