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.

翻译：单个不可分割物品的拍卖是带转移支付机制设计中最经典的问题之一。尽管结构简单，但该领域文献提供了最为清晰且富有洞察力的结果。当所有参与者均知晓拍卖信息时，Myerson [20]提出了刻画激励相容拍卖及最优收益的开创性结论。然而，该结论在网络化拍卖中并不成立——在此类拍卖中，信息通过代理人传播，需要设计激励促使他们传递信息。近期，部分研究（如 [13, 18]）设计了能够适当激励网络中间节点将信息传递给潜在价值更高竞拍者的拍卖机制。本文提出了网络环境下激励相容拍卖的类Myerson刻画，并证明现有已知拍卖均属于这类随机化拍卖的范畴。随后，我们借鉴多层次营销机制 [1, 6, 7] 的思路，聚焦一类特殊拍卖——推荐拍卖，推导出针对独立同分布竞拍者的最优收益推荐拍卖结构。实验表明，即使面对非独立同分布竞拍者，遵循该刻画的拍卖也能比现有网络拍卖获得更高收益。