We consider a multi-unit auction of identical items with single-minded bidders, where a subset of bidders may collude by coordinating bids and transferring payments and items among themselves. Classical collusion-proof mechanisms are largely restricted to posted-price formats, which fail to guarantee even approximate efficiency. We therefore adopt a learning-augmented approach to leverage side information about which bidders are colluding and obtain improved welfare and revenue guarantees. In our setting, colluding bidders optimally shade their bids to suppress prices. Using this characterization, we establish a Bulow-Klemperer type result showing that recruiting more honest bidders is better than the best collusion-proof auction mechanism. We then consider a setting in which a black-box collusion detection algorithm labels bidders as colluding or non-colluding, and propose a VCG Posted Price (V-PoP) mechanism that applies VCG to non-colluding bidders and posted prices to colluding bidders. We show that V-PoP is ex-post dominant-strategy incentive compatible (DSIC) even when it uses select bidder information to calculate an optimal split of items between the subgroups. Additionally, we derive probabilistic guarantees on expected welfare and revenue under both known and unknown valuation distributions, and analyze the robustness of V-PoP to bidder misclassification errors. Numerical experiments across several distributions demonstrate that V-PoP consistently outperforms VCG restricted to non-colluding bidders and approaches the performance of the ideal VCG mechanism assuming universal truthfulness. Our results provide a principled framework for incorporating collusion detection into mechanism design, advancing the theory of auctions under collusion.

翻译：我们考虑具有单值竞拍者的同质物品多单元拍卖，其中部分竞拍者可能通过协调报价及相互转移支付与物品来实施共谋。经典的防共谋机制主要局限于固定价格形式，这类机制甚至无法保证近似效率。为此，我们采用学习增强方法，通过利用关于哪些竞拍者参与共谋的辅助信息，来改进社会福利与收益保障。在我们的设定中，共谋竞拍者会通过压低报价来抑制价格。基于这一特征刻画，我们建立了Bulow-Klemperer型结果，表明招募更多诚实竞拍者优于最优的防共谋拍卖机制。随后我们考虑一种场景：黑箱式共谋检测算法为竞拍者标注共谋或非共谋标签，并提出了VCG固定价格机制（V-PoP），该机制对非共谋竞拍者应用VCG，对共谋竞拍者应用固定价格。我们证明，即使V-PoP需利用部分竞拍者信息来优化两个子群体间的物品分配方案，它仍能实现事后占优策略激励相容（DSIC）。此外，我们分别在已知与未知估值分布下推导了关于期望社会福利与收益的概率性保障，并分析了V-PoP对竞拍者误分类误差的鲁棒性。跨多个分布的数值实验表明，V-PoP持续优于仅面向非共谋竞拍者的VCG，且逼近假设全体竞拍者均诚实时理想VCG机制的性能。我们的研究为将共谋检测融入机制设计提供了系统性框架，推进了共谋环境下的拍卖理论发展。