# Selling to Multiple No-Regret Buyers

arXiv: https://arxiv.org/abs/2307.04175 · HTML: https://mlsanity.com/paper/2307.04175/

## Key facts

- Cited by 19 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 9 Jul 2023.

## Built on by (most cited first, 19 of 19)

- [Fast swap regret minimization and applications to approximate correlated equilibria](https://mlsanity.com/paper/2310.19647/) (2023)
- [Contracting with a Learning Agent](https://mlsanity.com/paper/2401.16198/) (2024)
- [Full Swap Regret and Discretized Calibration](https://mlsanity.com/paper/2502.09332/) (2025)
- [Strategizing against No-Regret Learners in First-Price Auctions](https://mlsanity.com/paper/2402.08637/) (2024)
- [Maximizing utility in multi-agent environments by anticipating the behavior of other learners](https://mlsanity.com/paper/2407.04889/) (2024)
- [Swap Regret and Correlated Equilibria Beyond Normal-Form Games](https://mlsanity.com/paper/2502.20229/) (2025)
- [Generalized Principal-Agent Problem with a Learning Agent](https://mlsanity.com/paper/2402.09721/) (2024)
- [Should Decision-Makers Reveal Classifiers in Online Strategic Classification?](https://mlsanity.com/paper/2506.01936/) (2025)
- [Rate-Preserving Reductions for Blackwell Approachability](https://mlsanity.com/paper/2406.07585/) (2024)
- [Games with Payments between Learning Agents](https://mlsanity.com/paper/2405.20880/) (2024)
- [Learning to Play Against Unknown Opponents](https://mlsanity.com/paper/2412.18297/) (2024)
- [Best of Both Worlds: Regret Minimization versus Minimax Play](https://mlsanity.com/paper/2502.11673/) (2025)
- [Computational Intractability of Strategizing against Online Learners](https://mlsanity.com/paper/2503.04202/) (2025)
- [From No-Regret to Strategically Robust Learning in Repeated Auctions](https://mlsanity.com/paper/2601.03853/) (2026)
- [Near-optimal Swap Regret Minimization for Convex Losses](https://mlsanity.com/paper/2602.08862/) (2026)
- [Randomized Truthful Auctions with Learning Agents](https://mlsanity.com/paper/2411.09517/) (2024)
- [Markets with Heterogeneous Agents: Dynamics and Survival of Bayesian vs. No-Regret Learners](https://mlsanity.com/paper/2502.08597/) (2025)
- [Learning Local Stackelberg Equilibria from Repeated Interactions with a Learning Agent](https://mlsanity.com/paper/2510.22471/) (2025)
- [Is Online Linear Optimization Sufficient for Strategic Robustness?](https://mlsanity.com/paper/2602.12253/) (2026)

## Abstract (arXiv)

We consider the problem of repeatedly auctioning a single item to multiple i.i.d buyers who each use a no-regret learning algorithm to bid over time. In particular, we study the seller's optimal revenue, if they know that the buyers are no-regret learners (but only that their behavior satisfies some no-regret property -- they do not know the precise algorithm/heuristic used). Our main result designs an auction that extracts revenue equal to the full expected welfare whenever the buyers are "mean-based" (a property satisfied by standard no-regret learning algorithms such as Multiplicative Weights, Follow-the-Perturbed-Leader, etc.). This extends a main result of [BMSW18] which held only for a single buyer. Our other results consider the case when buyers are mean-based but never overbid. On this front, [BMSW18] provides a simple LP formulation for the revenue-maximizing auction for a single-buyer. We identify several formal barriers to extending this approach to multiple buyers.