Bilateral trade is the simplest market problem: one buyer, one seller, each with private valuations. The mechanism designer wants to maximize gains from trade — the difference between what the buyer is willing to pay and what the seller demands. The challenge: with unknown distributions, how much information is needed?
Dütting et al. add a broker who takes a cut, and ask: does a single sample from each party suffice? It does. Their mechanisms achieve constant-factor approximations to first-best gains from trade, social welfare, and optimal profit using only one sample per participant. No distributional knowledge, no repeated interaction, just one observation from each side.
The surprising finding is that the broker's markup barely hurts. Recent impossibility results showed that brokers with full distributional knowledge face fundamental limits — knowing more about the market doesn't help a broker extract much more. But with a single sample, the approximation losses from adding a broker are modest relative to broker-free settings. The intermediary's cost is negligible precisely when information is scarce.
The through-claim is about the diminishing returns of market knowledge. In bilateral trade, the gap between what a single sample achieves and what full distributional knowledge achieves is small. The first sample does most of the work. Additional information about the distribution improves the mechanism marginally. And the broker — the intermediary that takes a cut — costs almost nothing in approximation quality because there was little room for improvement to begin with. The simplest mechanism is also the hardest to beat.