Single-Sample Bilateral Trade with a Broker

2026-03-03

AI Summary

This study addresses the design of single-sample two-sided trading mechanisms with an intermediary, under the stringent informational constraint that only one sample from each of the buyer’s and seller’s valuation distributions is available. Focusing on settings where the valuation distributions are either identical or satisfy stochastic dominance, the work proposes simple, incentive-compatible matching mechanisms. It is the first to extend single-sample mechanism design to environments involving an intermediary. Under the monotone hazard rate assumption, the proposed mechanisms achieve constant-factor approximations for social welfare, gains from trade, and intermediary profit—surmounting the inapproximability barrier that arises under full information when strategic intermediaries are present. Moreover, the paper establishes upper bounds that are either matching or nearly tight.

Technology Category

• Multiagent Systems: Mechanism Design
• Game Theory and Economic Paradigms: Mechanism Design
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Security and Privacy: Large-scale security measurements
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking

Abstract

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.

Problem

• bilateral trade
• broker
• single-sample
• informational constraints
• gains-from-trade

Innovation

• single-sample mechanism
• bilateral trade with broker
• gains-from-trade approximation
• monotone hazard rate
• data-efficient brokerage