Second-Best Bilateral Trade is $1/2$ Efficient
Resolves a long-standing open question in mechanism design about the efficiency loss in bilateral trade, providing a definitive tight bound.
The paper proves that the Bayesian-optimal mechanism for bilateral trade always achieves at least half of the first-best gains from trade, closing the gap between previous bounds of 0.317 and 0.736 with a tight result.
The landmark Myerson-Satterthwaite Theorem establishes a fundamental impossibility in bilateral trade: no Bayesian incentive-compatible mechanism can simultaneously achieve ex-post efficiency, individual rationality, and strong budget balance. We resolve a long-standing open question regarding the efficiency loss imposed by these constraints. Specifically, we prove that the Bayesian-optimal (second-best) mechanism always captures at least half of the first-best gains from trade ($\mathrm{SB}\ge\frac{1}{2}\mathrm{FB}$). This result is tight, definitively closing the gap between the previously best-known bounds of $0.317$ and $0.736$.