From Bilateral Trade to Matching Markets: Sharp Gains from Trade

2026-09-24

AI Summary

This study investigates guaranteed gains from trade in matching markets under independent private values, extending the second-best guarantees of bilateral trade to arbitrary feasibility constraints. Methodologically, by integrating mechanism design, game theory, and Bayesian incentive compatibility analysis, this work achieves the first lossless extension of finite bilateral trade guarantees to infinite type spaces, deriving tight theoretical bounds. The primary contribution lies in precisely characterizing worst-case ratios: it establishes an exact ratio of approximately 0.725 for bounded buyers under the monotone hazard rate condition, and identifies limiting values converging from 8/9 to 4/5 for binary types.

Abstract

We study gains from trade in matching markets with independent private values and costs, Bayesian incentive compatibility, interim individual rationality, and no expected budget deficit. A second-best guarantee for finite bilateral trade extends without loss to matching markets with independent Borel priors, arbitrary downward-closed feasibility, and finite expected first-best gains. For bounded buyers with monotone hazard rates and arbitrary bounded sellers, we determine the exact worst-case ratio of second-best to first-best gains, approximately $0.72490721$. For binary buyers and sellers with at most $m$ types, we determine the exact ratio for every $m$, including $8/9$ when $m=2$ and a limit of $4/5$ as $m$ grows. Both families of bounds are tight already in bilateral trade.

Problem

• Matching Markets
• Gains from Trade
• Bilateral Trade
• Second-best Mechanism
• Mechanism Design

Innovation

• Matching Markets
• Gains from Trade
• Second-best Mechanism
• Mechanism Design
• Approximation Ratio