Optimal Referral Auction Design

The auction of a single indivisible item is one of the most celebrated problems in mechanism design with transfers. Despite its simplicity, it provides arguably the cleanest and most insightful results in the literature. When the information that the auction is running is available to every participant, Myerson [20] provided a seminal result to characterize the incentive-compatible auctions along with revenue optimality. However, such a result does not hold in an auction on a network, where the information of the auction is spread via the agents, and they need incentives to forward the information. In recent times, a few auctions (e.g., [13, 18]) were designed that appropriately incentivized the intermediate nodes on the network to promulgate the information to potentially more valuable bidders. In this paper, we provide a Myerson-like characterization of incentive-compatible auctions on a network and show that the currently known auctions fall within this class of randomized auctions. We then consider a special class called the referral auctions that are inspired by the multi-level marketing mechanisms [1, 6, 7] and obtain the structure of a revenue optimal referral auction for i.i.d. bidders. Through experiments, we show that even for non-i.i.d. bidders there exist auctions following this characterization that can provide a higher revenue than the currently known auctions on networks.