An Improved Upper Bound for the Random-Offerer Mechanism in Bilateral Trade via Recursive Hard Instances

2026-10-05

AI Summary

This study addresses the problem of establishing upper bounds on the worst-case efficiency ratio of randomized pricing mechanisms in bilateral trade. To this end, it proposes a hard instance construction strategy that recursively nests seller distributions with downward transmission of buyer valuations, leveraging multi-scale recursive structures to accumulate contributions. By integrating optimal transport theory with recurrence relation analysis techniques, the approach generates stronger hard instances capable of surpassing existing theoretical limits. As a result, this work significantly improves the upper bound on the efficiency ratio from 0.4602 to approximately 0.4369, providing a tighter theoretical characterization for understanding the fundamental efficiency limits of such mechanisms.

Abstract

We study the worst-case efficiency of the random-offerer mechanism in bilateral trade relative to the first-best gains from trade. We construct a family of independent buyer value and seller cost distributions whose ratio converges to $0.436943488\ldots$, improving the previous upper bound of $0.460242308\ldots$. Our construction combines recursively nested seller distributions with downward transport of buyer values. The recursive structure allows contributions from different scales to accumulate, leading to stronger hard instances. We analyze this construction through a recurrence and obtain an analytic characterization of the limiting constant.

Problem

• bilateral trade
• random-offerer mechanism
• worst-case efficiency
• upper bound
• gains from trade

Innovation

• Bilateral Trade
• Random-Offerer Mechanism
• Recursive Hard Instances
• Approximation Ratio
• Mechanism Design