Do Not Trust The Auctioneer: Learning to Bid in Feedback-Manipulated Auctions

2026-05-21

AI Summary

This study addresses the problem of online bidding in repeated first-price auctions where feedback is manipulated by fake bids that leave allocation outcomes unchanged. The authors propose an adaptive algorithm that integrates robust interval elimination with optimistic debiased estimation, enabling dynamic switching between learning strategies without prior knowledge of the feedback structure. They establish, for the first time, that manipulating only the feedback can substantially increase the statistical complexity of the problem. Under known distributions of fake bids, the algorithm achieves regret upper bounds of either Õ(√T) or Õ(T^{2/3}), depending on the setting. Furthermore, in the single-active-region scenario, they prove a matching lower bound, thereby establishing the theoretical optimality of their approach.

Abstract

Shilling is the use of artificial bids to make competition appear stronger and push prices upward. We study repeated first-price auctions in which shilling affects feedback but not allocation: the learner wins or loses against the real competing bid, but after a loss observes the maximum of the real bid and an independent shill bid. Thus the manipulation changes what the learner observes and hence how it learns to bid, without changing the outcome of the current auction. We analyze regret with respect to the best bid benchmark, assuming that the shill-bid distribution is known. Even then, shilling can mask the real bid, while useful side information appears only through intermittent low-shill events. Our algorithm combines a robust interval-elimination branch, which ignores the shilled report and achieves the dynamic-pricing rate $\tilde{\mathcal{O}}(T^{2/3})$, with an optimistic branch that debiases losing-side reports and exploits the resulting suffix information when it is reliable and achieves the first-price auctions rate $\tilde{\mathcal{O}}(\sqrt{T})$. A validation and racing procedure lets the algorithm use these optimistic updates without knowing the right scale or feedback geometry in advance. We complement the upper bounds with a matching lower bound, up to logarithmic factors, in the single-active-region case. Overall, the results show that even feedback-only shilling can sharply alter the statistical difficulty of repeated bidding.

Problem

• shilling
• first-price auctions
• feedback manipulation
• online learning
• regret minimization

Innovation

• shilling
• first-price auctions
• feedback manipulation
• regret minimization
• adaptive learning