# Fixed-Price Approximations in Bilateral Trade

arXiv: https://arxiv.org/abs/2107.14327 · HTML: https://mlsanity.com/paper/2107.14327/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 29 Jul 2021.

## Built on by (most cited first, 10 of 10)

- [No-Regret Learning in Bilateral Trade via Global Budget Balance](https://mlsanity.com/paper/2310.12370/) (2023)
- [An Online Learning Theory of Brokerage](https://mlsanity.com/paper/2310.12107/) (2023)
- [Nearly Tight Regret Bounds for Profit Maximization in Bilateral Trade](https://mlsanity.com/paper/2509.22563/) (2025)
- [Learning to Maximize Gains From Trade in Small Markets](https://mlsanity.com/paper/2401.11596/) (2024)
- [A Parametric Contextual Online Learning Theory of Brokerage](https://mlsanity.com/paper/2407.01566/) (2024)
- [A Tight Regret Analysis of Non-Parametric Repeated Contextual Brokerage](https://mlsanity.com/paper/2503.02646/) (2025)
- [Nonparametric Contextual Online Bilateral Trade](https://mlsanity.com/paper/2602.12904/) (2026)
- [A New Lower Bound for the Random Offerer Mechanism in Bilateral Trade using AI-Guided Evolutionary Search](https://mlsanity.com/paper/2603.08679/) (2026)
- [Trading Volume Maximization with Online Learning](https://mlsanity.com/paper/2405.13102/) (2024)
- [Regret Minimization in Bilateral Trade With Perturbed Markets](https://mlsanity.com/paper/2605.10475/) (2026)

## Abstract (arXiv)

We consider the bilateral trade problem, in which two agents trade a single indivisible item. It is known that the only dominant-strategy truthful mechanism is the fixed-price mechanism: given commonly known distributions of the buyer's value B and the seller's value S, a price p is offered to both agents and trade occurs if S ≤ p ≤ B. The objective is to maximize either expected welfare mathbbE[S + (B-S) 1S ≤ p ≤ B] or expected gains from trade mathbbE[(B-S) 1S ≤ p ≤ B]. We improve the approximation ratios for several welfare maximization variants of this problem. When the agents' distributions are identical, we show that the optimal approximation ratio for welfare is frac2+√24. With just one prior sample from the common distribution, we show that a 3/4-approximation to welfare is achievable. When agents' distributions are not required to be identical, we show that a previously best-known (1-1/e)-approximation can be strictly improved, but 1-1/e is optimal if only the seller's distribution is known.