Second-Best Bilateral Trade is $1/2$ Efficient

2026-06-02

AI Summary

This study addresses the fundamental efficiency limits of bilateral trade under Bayesian incentive compatibility, ex-post individual rationality, and strong budget balance. Building upon the impossibility result of Myerson and Satterthwaite, the authors employ tools from Bayesian mechanism design, information economics, and extremal analysis, together with carefully constructed valuation distributions for buyer and seller, to rigorously establish that any feasible mechanism achieves an expected gains-from-trade of at least one-half of the first-best benchmark. This result closes a long-standing gap in the literature, where prior bounds ranged between approximately 0.317 and 0.736, and demonstrates that the factor-of-two bound is tight. Consequently, the work precisely characterizes the minimal efficiency loss inherent in bilateral trade, resolving a central open question in the field.

Abstract

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 $0.736$.

Problem

• bilateral trade
• Myerson-Satterthwaite Theorem
• efficiency loss
• second-best mechanism
• first-best gains

Innovation

• bilateral trade
• Myerson-Satterthwaite Theorem
• second-best mechanism
• efficiency bound
• Bayesian incentive compatibility