We introduce the groupwise-pivotal referral (GPR) mechanism for auctions where buyers can participate through referrals. Each buyer's type consists of a valuation and referable buyers. Unlike the second-price auction (SPA), the Vickrey-Clarke-Groves (VCG) mechanism provides referral incentives. However, VCG is not budget-feasible. In contrast, under complete information, GPR is core-selecting, implying efficiency and budget feasibility. Under incomplete information, bidders refer truthfully and have no incentive to underbid in GPR. Furthermore, GPR's ex-post revenue outperforms both VCG and SPA, not just in equilibrium but also when bidders do not use weakly dominated strategies.

我们引入了拍卖的分组关键推荐（GPR）机制，买家可以通过推荐参与拍卖。每个买家类型由估价和推荐买家组成。与次价拍卖 (SPA) 不同，Vickrey-Clarke-Groves (VCG) 机制提供推荐激励。然而，VCG 在预算上并不可行。相比之下，在完全信息下，探地雷达是选芯的，意味着效率和预算可行性。在信息不完整的情况下，投标人如实反映，没有动机在 GPR 中低价出价。此外，GPR 的事后收入优于 VCG 和 SPA，不仅在均衡状态下，而且在投标人不使用弱支配策略时也是如此。