Collusion-proof Auction Design using Side Information

TL;DR

This paper introduces collusion-proof auction mechanisms using machine learning classifiers to predict colluding bidders, ensuring truthfulness and robustness against collusion with theoretical bounds and numerical validation.

Contribution

It proposes two novel truthful auction mechanisms, V-PoP and C-PoP, leveraging classifiers to mitigate collusion effects and provides theoretical bounds under classifier errors.

Findings

Mechanisms achieve high welfare and revenue against collusion.

False negatives in classifiers are less harmful than false positives.

Theoretical bounds guide classifier design for better auction outcomes.

Abstract

Existing auction mechanisms are vulnerable to bidder collusion, which substantially degrades revenue and non-colluder welfare. To design truthful mechanisms resilient to collusion, we introduce a novel approach that leverages a machine learning classifier to predict (even imprecisely) which bidders are colluding. We first establish a Bulow-Klemperer-type result for multi-unit auctions with single-minded bidders, demonstrating that collusion significantly harms existing mechanisms only when the colluding coalition is large. Consequently, we focus our design on settings with many colluders. Building on the welfare-optimal Vickrey-Clarke-Groves (VCG) mechanism, we propose two novel truthful mechanisms: VCG-Posted Price (V-PoP) and Conditional-Posted Price (C-PoP). V-PoP applies VCG to non-colluding bidders and posted prices to colluding ones, and ensuring truthfulness is non-trivial because we must dynamically split the quantity of items between these groups based on the values of the non-colluder bids. C-PoP further advances this by computing a posted price conditioned on non-colluder bids, and ensuring truthfulness is non-obvious because the posted price is chosen using the values of the non-colluder bids. Because real-world classifiers make errors, we provide theoretical lower bounds on the auction price of V-PoP and C-PoP under misclassification, which theory shows acts as a proxy for welfare and revenue. Crucially, our bounds yield actionable insights for classifier design, revealing that false negatives (misclassifying colluders as non-colluders) are preferable to false positives (misclassifying non-colluders as colluders). Numerical experiments demonstrate that our mechanisms achieve high welfare and revenue against collusion, even when utilizing simple, low-cost classifiers.