Collusion-proof Auction Design using Side Information

We study the problem of auction design in the presence of bidder collusion. Specifically, 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. The classical Vickrey-Clarke-Groves(VCG) mechanism is highly vulnerable to collusion and fully collusion-proof mechanisms are limited to posted-price formats, which fail to guarantee even approximate efficiency. This paper aims to bridge this gap by designing auctions that achieve good welfare and revenue guarantees even when some bidders collude. We first characterize the strategic behavior of colluding bidders under VCG and prove that such bidders optimally bid shade: they never overbid or take additional items, but instead reduce the auction price. This characterization enables a Bulow-Klemperer type result: adding colluding bidders can only improve welfare and revenue relative to running VCG on the non-colluding group alone. We next consider a setting where black-box collusion detection algorithm is available to label bidders as being colluding or non-colluding, and we propose a VCG-Posted Price(V-PoP) mechanism that combines VCG applied to non-colluding bidders with a posted-price mechanism for colluding bidders. We show that V-PoP is ex-post dominant-strategy incentive compatible(DSIC) and derive probabilistic guarantees on expected welfare and revenue under both known and unknown valuation distributions. 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, offering a step toward collusion-resistant auctions.