We initiate the study of single-sample bilateral trade with a broker, drawing an analogy to the setting of single-sample bilateral trade without a broker considered in Babaioff et al. (2020) and Cai and Wu (2023). Our model captures the three-sided interaction in which a broker mediates trade between a buyer and seller, each described by a valuation distribution from which a single sample can be drawn. We consider two settings in particular: one where the valuation distributions of the buyer and seller are identical and one where the valuation distributions are stochastically ordered. We analyze simple mechanisms that rely only on a single sample from each agent's distribution and show that these mechanisms achieve constant-factor approximations to the first-best gains-from-trade (GFT), first-best social welfare (SW), and optimal profit under the standard monotone-hazard-rate assumption. We then complement these results with matching or nearly matching upper bounds on the GFT and SW of our mechanisms. Notably, in both settings, we observe fairly small losses in the approximation factors to the first-best GFT and first-best SW due to the existence of the broker (benchmarked against the corresponding approximation factors in the setting without a broker). Furthermore, our results stand in stark contrast to those of Hajiaghayi et al. (2025), who show inapproximability results under a strategic broker with full distributional knowledge. Our results provide insight into the design of data-efficient brokerage mechanisms for online marketplaces and decentralized trading platforms, where intermediaries must facilitate trade under severe informational constraints. They highlight how even minimal data can enable robust and incentive-compatible brokerage in uncertain markets for both the broker and the market participants.

翻译：本文首次研究了存在经纪人的单样本双边交易问题，与Babaioff等人（2020）及Cai和Wu（2023）所考察的无经纪人单样本双边交易场景形成类比。我们的模型刻画了经纪人作为中介协调买卖双方交易的三方互动场景，其中买卖双方的价值分布均可通过单一样本进行估计。我们重点考察两种特定情境：一是买卖双方价值分布相同的情形，二是价值分布存在随机序关系的情形。我们分析了仅依赖各参与方分布单一样本的简单机制，并证明在标准单调风险率假设下，这些机制能够以常数因子逼近最优交易收益、最优社会福利以及最优利润。随后，我们通过匹配或近似匹配的上界结果，补充说明了所提出机制在交易收益和社会福利方面的理论边界。值得注意的是，在这两种情境中，相较于无经纪人场景下的对应近似因子，由于经纪人的存在所导致的交易收益和社会福利近似因子损失均相对较小。此外，我们的结论与Hajiaghayi等人（2025）的研究形成鲜明对比——后者在经纪人拥有完全分布信息且具有策略性的条件下证明了不可逼近性结果。本研究为在线市场和去中心化交易平台中数据高效的经纪人机制设计提供了理论依据，这类场景中中介机构必须在严苛的信息约束下促成交易。我们的成果揭示了即使仅凭极少量的数据，也能为经纪人及市场参与者在不确定性市场中实现稳健且激励相容的中介服务。