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 $0.736$.

翻译：标志性的迈尔森-萨特思韦特定理揭示了双边贸易中的一个基本不可能性：没有任何贝叶斯激励相容机制能同时实现事后效率、个体理性与强预算平衡。本文解决了关于这些约束所导致效率损失的长期悬而未决的问题。具体而言，我们证明贝叶斯最优（次优）机制始终能捕获至少一半的一阶最优贸易收益（$\mathrm{SB}\ge\frac{1}{2}\mathrm{FB}$）。该结果是紧的，最终填补了先前已知最优界限 $0.317$ 与 $0.736$ 之间的差距。