# Fair Online Bilateral Trade

arXiv: https://arxiv.org/abs/2405.13919 · HTML: https://mlsanity.com/paper/2405.13919/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 25 references that are in the map.
- First posted on arXiv 22 May 2024.

## Builds on (most cited first, 17 of 17)

- [Achieving Fairness in the Stochastic Multi-armed Bandit Problem](https://mlsanity.com/paper/1907.10516/) (2019)
- [Combinatorial Sleeping Bandits with Fairness Constraints](https://mlsanity.com/paper/1901.04891/) (2019)
- [Online Learning with an Unknown Fairness Metric](https://mlsanity.com/paper/1802.06936/) (2018)
- [Fairness of Exposure in Stochastic Bandits](https://mlsanity.com/paper/2103.02735/) (2021)
- [Fair Algorithms for Multi-Agent Multi-Armed Bandits](https://mlsanity.com/paper/2007.06699/) (2020)
- [Equal Opportunity in Online Classification with Partial Feedback](https://mlsanity.com/paper/1902.02242/) (2019)
- [Bilateral Trade: A Regret Minimization Perspective](https://mlsanity.com/paper/2109.12974/) (2021)
- [A Regret Analysis of Bilateral Trade](https://mlsanity.com/paper/2102.08754/) (2021)
- [No-Regret Learning in Bilateral Trade via Global Budget Balance](https://mlsanity.com/paper/2310.12370/) (2023)
- [Online Fair Division: A Survey](https://mlsanity.com/paper/1911.09488/) (2019)
- [An α-regret analysis of Adversarial Bilateral Trade](https://mlsanity.com/paper/2210.06846/) (2022)
- [Repeated Bilateral Trade Against a Smoothed Adversary](https://mlsanity.com/paper/2302.10805/) (2023)
- [On preserving non-discrimination when combining expert advice](https://mlsanity.com/paper/1810.11829/) (2018)
- [A Nearest Neighbor Characterization of Lebesgue Points in Metric Measure Spaces](https://mlsanity.com/paper/2007.03937/) (2020)
- [An Online Learning Theory of Brokerage](https://mlsanity.com/paper/2310.12107/) (2023)
- [Nonstationary Dual Averaging and Online Fair Allocation](https://mlsanity.com/paper/2202.11614/) (2022)
- [The price of unfairness in linear bandits with biased feedback](https://mlsanity.com/paper/2203.09784/) (2022)

## Built on by (most cited first, 4 of 4)

- [Market Making without Regret](https://mlsanity.com/paper/2411.13993/) (2024)
- [A Tight Regret Analysis of Non-Parametric Repeated Contextual Brokerage](https://mlsanity.com/paper/2503.02646/) (2025)
- [Regret Minimization in Bilateral Trade With Perturbed Markets](https://mlsanity.com/paper/2605.10475/) (2026)
- [Breaking the T3/4 Barrier for Regret Minimization With Bi-Dimensional CDFs](https://mlsanity.com/paper/2607.20258/) (2026)

## Abstract (arXiv)

In online bilateral trade, a platform posts prices to incoming pairs of buyers and sellers that have private valuations for a certain good. If the price is lower than the buyers' valuation and higher than the sellers' valuation, then a trade takes place. Previous work focused on the platform perspective, with the goal of setting prices maximizing the gain from trade (the sum of sellers' and buyers' utilities). Gain from trade is, however, potentially unfair to traders, as they may receive highly uneven shares of the total utility. In this work we enforce fairness by rewarding the platform with the fair gain from trade, defined as the minimum between sellers' and buyers' utilities. After showing that any no-regret learning algorithm designed to maximize the sum of the utilities may fail badly with fair gain from trade, we present our main contribution: a complete characterization of the regret regimes for fair gain from trade when, after each interaction, the platform only learns whether each trader accepted the current price. Specifically, we prove the following regret bounds: Theta(ln T) in the deterministic setting, Omega(T) in the stochastic setting, and tildeTheta(T2/3) in the stochastic setting when sellers' and buyers' valuations are independent of each other. We conclude by providing tight regret bounds when, after each interaction, the platform is allowed to observe the true traders' valuations.