From No-Regret to Strategically Robust Learning in Repeated Auctions

2026-01-07

arXiv.org

AI Summary

This work addresses the challenge of simultaneously achieving no-regret performance and strategic robustness in repeated auctions while ensuring the auctioneer’s revenue does not exceed Myerson’s optimal benchmark. The authors propose a monotone bidding strategy based on quantized space representations, which embeds any no-regret learning algorithm—such as Multiplicative Weights Update (MWU) or adaptive Online Gradient Descent—into an auction mechanism that satisfies allocation monotonicity and voluntary participation, thereby guaranteeing strategic robustness under dynamic reserve prices. The key theoretical contribution lies in establishing a fundamental connection between standard no-regret learning and strategic robustness: any no-regret algorithm operating over a quantized representation inherently satisfies strategic robustness without explicitly optimizing for swap regret. Notably, the MWU algorithm achieves both the optimal regret bound and the strongest known strategic robustness guarantee, applicable to any per-round auction format meeting mild regularity conditions.

Technology Category

• Multiagent Systems: Mechanism Design
• Game Theory and Economic Paradigms: Mechanism Design
• Machine Learning: Online Learning & Bandits

Application Category

• Economics, Online Markets and Human Computation: Uses of LLMs and GenAI for marketplace design, bidding, and strategic interactions
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods

Abstract

In Bayesian single-item auctions, a monotone bidding strategy--one that prescribes a higher bid for a higher value type--can be equivalently represented as a partition of the quantile space into consecutive intervals corresponding to increasing bids. Kumar et al. (2024) prove that agile online gradient descent (OGD), when used to update a monotone bidding strategy through its quantile representation, is strategically robust in repeated first-price auctions: when all bidders employ agile OGD in this way, the auctioneer's average revenue per round is at most the revenue of Myerson's optimal auction, regardless of how she adjusts the reserve price over time. In this work, we show that this strategic robustness guarantee is not unique to agile OGD or to the first-price auction: any no-regret learning algorithm, when fed gradient feedback with respect to the quantile representation, is strategically robust, even if the auction format changes every round, provided the format satisfies allocation monotonicity and voluntary participation. In particular, the multiplicative weights update (MWU) algorithm simultaneously achieves the optimal regret guarantee and a strong strategic robustness guarantee in this auction setting. At a technical level, our results are established via a simple relation that bridges Myerson's auction theory and standard no-regret learning theory.

Problem

• strategic robustness
• no-regret learning
• repeated auctions
• allocation monotonicity
• voluntary participation

Innovation

• strategic robustness
• no-regret learning
• quantile representation
• Myerson auction
• multiplicative weights update