Single-Sample Bilateral Trade with a Broker
MohammadTaghi Hajiaghayi, Gary Peng, Suho Shin

TL;DR
This paper studies single-sample bilateral trade with a broker, showing simple mechanisms can approximate optimal trade gains and welfare under informational constraints, contrasting with inapproximability results for strategic brokers.
Contribution
Introduces a model for single-sample bilateral trade with a broker, analyzing mechanisms that achieve constant-factor approximations to optimal outcomes under minimal data.
Findings
Mechanisms achieve constant-factor approximation to first-best GFT and SW.
Small losses in approximation due to broker presence compared to no-broker setting.
Contrasts with inapproximability results for strategic brokers with full knowledge.
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…
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Taxonomy
TopicsAuction Theory and Applications · Game Theory and Voting Systems · Game Theory and Applications
