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

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.

• The paper introduces an algorithm combining robust interval elimination and optimistic cross-learning to counteract shill bid manipulation.
• It demonstrates that debiasing losing-side reports can recover faster learning rates by exploiting intermittent, informative feedback.
• Theoretical analysis establishes tight regret bounds, bridging the gap between dynamic pricing and standard first-price auction learning.

Learning Bids under Manipulated Feedback in First-Price Auctions

Problem Formulation and Feedback Manipulation

The paper "Do Not Trust The Auctioneer: Learning to Bid in Feedback-Manipulated Auctions" (2605.22438) investigates learning-theoretic aspects of repeated first-price auctions in the presence of max-shilling feedback corruption. In this model, an auction platform injects artificial shill bids into post-auction feedback: losing bidders observe the maximum of the true highest competing bid and an independent shill bid, rather than the truthful highest competing bid. Crucially, the auction outcome remains determined by the real bids only—the feedback channel alone is corrupted. This distinction models scenarios in which platforms shape bidder learning by altering only observable auction feedback, not the allocation rules.

The core technical challenge induced by this feedback manipulation is the loss or attenuation of cross-learning above the bidder’s chosen value, a property that otherwise enables fast no-regret rates in standard first-price auction learning, contrasting with the inherently more myopic information structure in dynamic pricing setups.

Model and Regret Benchmarks

The learner’s value at round $t$ is $v_t\in [0,1]$, and their chosen bid $p_t$ competes with a (random) highest real bid $b_t$ and an independent shill bid $s_t$ (both drawn from unknown but fixed distributions). If $p_t\geq b_t$, the learner wins and receives reward $(v_t - p_t)$; otherwise, the learner observes the shilled report $o_t = \max\{b_t, s_t\}$. The regret $R_T$ is measured with respect to the optimal fixed bidding strategy given the realized value sequence and the true (unmanipulated) competing bid distribution.

A significant observation is that uninformed learners ("trusting" the reported maximum) receive a censored view: the empirical CDF under the shilled feedback appears stochastically larger, misleading them to infer more aggressive competition, thus biasing subsequent bids upward.

Algorithmic Approach

To adapt to this corrupted and intermittent feedback channel, the authors propose an algorithm that combines two branches:

1. Robust Interval Elimination:

This component essentially ignores the extra information in shilled losing reports, relying only on win/loss events. It recovers the $O(T^{2/3})$ regret rate known from dynamic pricing, where only local information is available.

2. Optimistic Cross-Learning Using Suffix Information:

The key technical insight is that when the shill bid is lower than the highest real competing bid, the losing-side report exposes suffix information about the competitor's bid distribution (i.e., information about larger bids). By debiasing these losing-side reports utilizing the known shill distribution, the algorithm extracts intermittent cross-learning, regaining faster rates when the shill process admits frequent informative events.

An adaptive validation mechanism dynamically selects whether to trust the optimistic branch, based on statistical regularity conditions; otherwise, it falls back to the robust branch.

Theoretical Guarantees

The main results quantify the statistical price of feedback-only shilling:

1. Upper Bound (Single-Region Case):

The paper proves that, when the shill distribution satisfies mild regularity on the relevant regions and the set of "active" bid intervals can be covered by a single region ($v_t\in [0,1]$0), the minimax regret satisfies

$v_t\in [0,1]$1

where $v_t\in [0,1]$2 is (roughly) the minimum probability of observing an informative low-shill event on the active interval.

2. Lower Bound (Single-Region Case):

The authors construct a lower bound instance matching the above upper bound up to logarithmic factors, showing that interpolation between the dynamic pricing rate ($v_t\in [0,1]$3) and the optimal first-price rate (modified to include the $v_t\in [0,1]$4 dependence) is unavoidable: the order $v_t\in [0,1]$5 is tight under feedback-only shilling.

3. Multiple Region Case:

For $v_t\in [0,1]$6 (multiple disjoint active bid regions), the regret guarantee degrades to $v_t\in [0,1]$7, although matching lower bounds for this setting are left open due to increased complexity caused by informative leaking across regions through losing-side reports.

The analysis employs geometric and statistical tools to precisely characterize how suffix information, masked or revealed by the shill, influences what can be confidently learned about the utility curve.

Implications and Discussion

This work formalizes the intuition that information leakage, even when rare and transient, can substantially accelerate learning in auction environments—provided one exploits the correlation structure of observable feedback and understands the underlying shill process.

Practical Implications:

• Bidder Strategy Design: Robust algorithms can mitigate bias from platforms that strategically manipulate only the information channel rather than the allocation, which has practical significance for online markets subject to unobservable policy changes.
• Auction Platform Regulation: The work motivates stronger transparency and auditing of auction feedback mechanisms in digital marketplaces, as feedback-only manipulation can sharply alter statistical learning rates without being directly observable in outcomes.

Theoretical Directions:

• The study opens avenues for further work on feedback manipulation beyond independent shilling, including (a) adaptive or history-dependent shills, (b) unknown shill distributions, and (c) more complex auction mechanisms.
• A key unresolved direction is tight lower bounds in the presence of multiple active bid regions, which would necessitate refined information flows accounting for the global structure of feedback in high-dimensional action spaces.

Conclusion

The paper rigorously characterizes the learning-theoretic consequences of feedback-only shilling in repeated auction environments, providing sharp stochastic regret bounds and algorithms that interpolate smoothly between minimax regret rates of dynamic pricing and first-price auction learning. The results demonstrate how feedback manipulation—absent any change in allocation—presents fundamental challenges for efficient online learning, and provide a principled foundation for robust bidding strategies in non-credible auction environments (2605.22438).