Collusion-proof Auction Design using Side Information

2025-11-15

AI Summary

This paper addresses mechanism design for multi-unit homogeneous-item auctions under partial bidder collusion. While the classic VCG mechanism is efficient and incentive-compatible, it is highly vulnerable to collusion; conversely, fully collusion-proof mechanisms are restricted to fixed-price schemes, sacrificing efficiency. To bridge this gap, we propose a hybrid VCG mechanism: it retains VCG pricing for non-colluding bidders while applying customized pricing rules for detected collusive coalitions. Crucially, collusion detection—performed via black-box algorithms augmented with game-theoretic analysis—is tightly integrated into the mechanism design. Under incentive compatibility, our framework provides probabilistic approximation guarantees on both social welfare and seller revenue. Experiments across diverse value distributions demonstrate that our mechanism significantly outperforms a baseline that applies VCG only to non-colluding bidders, and closely approaches the efficiency and revenue of the ideal (uncolluded) VCG outcome.

Technology Category

• Game Theory and Economic Paradigms: Mechanism Design
• Multiagent Systems: Mechanism Design
• Search and Optimization: Mixed Discrete/Continuous Search

Application Category

• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• User Modeling, Personalization and Recommendation: Attacks and countermeasures in recommendation systems
• Security and Privacy: Large-scale security measurements

Abstract

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. While the classical Vickrey-Clarke-Groves (VCG) mechanism achieves efficient and truthful outcomes, it is highly vulnerable to collusion. In contrast, 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 then propose a Hybrid VCG (H-VCG) mechanism that combines VCG applied to non-colluding bidders with a posted-price mechanism for colluding bidders, assuming access to a black-box collusion detection algorithm. We show that H-VCG 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 H-VCG 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.

Problem

• Designing auctions resistant to bidder collusion while maintaining efficiency
• Characterizing strategic collusive behavior in multi-unit VCG auctions
• Developing hybrid mechanisms with welfare guarantees using collusion detection

Innovation

• Hybrid VCG mechanism combining VCG and posted-price
• Collusion detection algorithm for identifying colluding bidders
• Ex-post dominant-strategy incentive compatible auction design