Second-Best Bilateral Trade is $1/2$ Efficient
2026-06-02 • Computer Science and Game Theory
Computer Science and Game Theory
AI summaryⓘ
The authors address a problem in economics about trading between two parties where it's impossible to make a system that is perfectly efficient, fair, and budget-neutral all at once. They focus on how much efficiency must be lost because of this impossibility. They prove that the best possible mechanism still achieves at least half of the maximum potential gains from trade, which improves on previous estimates and settles the question exactly.
Myerson-Satterthwaite Theorembilateral tradeBayesian incentive-compatibilityex-post efficiencyindividual rationalitystrong budget balancemechanism designsecond-best mechanismgains from trade
Authors
Zhengyang Liu, Ying Qin, Zeyu Ren, Zihe Wang
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 $0.736$.