Second-Best Gains from Trade in Matching Markets

2026-09-16

AI Summary

研究匹配市场中独立私有类型下的贸易收益，通过贝叶斯激励兼容和强预算平衡机制证明了次优贸易收益至少为最优的一半。

Abstract

We study gains from trade (GFT) in two-sided matching markets with independent private types and arbitrary downward-closed feasibility constraints. The second-best benchmark is the maximum expected GFT achievable by a Bayesian incentive compatible, interim individually rational mechanism that is strongly budget balanced at every report profile. These constraints generally preclude attaining the first-best GFT and raise the question of how much efficiency must be lost. We prove that the second-best GFT is at least one half of the first-best GFT in every such matching market. This recovers and generalizes the recent $1/2$ guarantee for bilateral trade by Liu et al. (2026) to markets with multiple buyers and sellers and arbitrary downward-closed feasibility constraints. Together with their matching lower bound for bilateral trade, our result establishes a tight worst-case ratio of $1/2$ for this general class of matching markets. Our proof builds on the virtual-GFT framework of Brüstle et al. (EC 2017) to reduce the problem to a one-parameter Lagrangian. The main step is a geometric, edge-by-edge analysis based on first-best edge-selection regions, combined with a randomized contraction in rank space.

Problem

• Second-Best Gains from Trade
• Two-Sided Matching Markets
• Feasibility Constraints
• Bayesian Incentive Compatibility
• Strong Budget Balance

Innovation

• second-best GFT
• matching markets
• downward-closed feasibility constraints
• Bayesian incentive compatibility
• virtual-GFT framework