Approximately Efficient Bilateral Trade with Samples

We study the social efficiency of bilateral trade between a seller and a buyer. In the classical Bayesian setting, the celebrated Myerson-Satterthwaite impossibility theorem states that no Bayesian incentive-compatible, individually rational, and budget-balanced mechanism can achieve full efficiency. As a counterpoint, Deng, Mao, Sivan, and Wang (STOC 2022) show that if pricing power is delegated to the right person (either the seller or the buyer), the resulting mechanism can guarantee at least a constant fraction of the ideal (yet unattainable) gains from trade. In practice, the agent with pricing power may not have perfect knowledge of the value distribution of the other party, and instead may rely on samples of that distribution to set a price. We show that for a broad class of sampling and pricing behaviors, the resulting market still guarantees a constant fraction of the ideal gains from trade in expectation. Our analysis hinges on the insight that social welfare under sample-based pricing approximates the seller's optimal revenue -- a result we establish via a reduction to a random walk.