This paper studies a mechanism design problem over a network, where agents can only participate by referrals. The Bulow-Klemberer theorem proposes that expanding the number of participants is a more effective approach to increase revenue than modifying the auction format. However, agents lack the motivation to invite others because doing so intensifies competition among them. On the other hand, misreporting social networks is also a common problem that can reduce revenue. Examples of misreporting include Sybil attacks (an agent pretending to be multiple bidders) and coalition groups (multiple agents pretending to be an agent). To address these challenges, we introduce a novel mechanism called the Truthful Referral Diffusion Mechanism (TRDM). TRDM incentivizes agents to report their social networks truthfully, and some of them are rewarded by the seller for improving revenue. In spite of the fact that some agents overbid in TRDM, the revenue is fixed, and it is higher than the revenue of any mechanism without referrals. TRDM is budget-balanced (non-negative revenue) and generates an efficient outcome (maximized social welfare), making it attractive for both the seller and the buyers as it improves revenue and reward.

翻译：本文研究了一个基于网络的机制设计问题，其中代理只能通过推荐参与。Bulow-Klemberer定理指出，扩大参与者数量比修改拍卖形式更能有效增加收益。然而，代理缺乏邀请他人的动机，因为这会加剧他们之间的竞争。另一方面，虚报社交网络也是一个常见问题，会降低收益。虚报的例子包括Sybil攻击（一个代理冒充多个竞拍者）和联盟团体（多个代理冒充一个代理）。为了解决这些挑战，我们提出了一种新颖的机制，称为诚实推荐扩散机制（TRDM）。TRDM激励代理如实报告其社交网络，其中一些代理因改善收益而获得卖家的奖励。尽管TRDM中存在部分代理出价过高的情况，但收益是固定的，且高于任何无推荐的机制的收益。TRDM具有预算平衡性（非负收益）并产生高效结果（最大化社会福利），这使得它对卖家和买家都具有吸引力，因为它既提高了收益又提供了奖励。