AI 中文总结
本文证明在具有任意向下封闭可行性约束的双边匹配市场中，次优贸易收益至少为最优贸易收益的一半，并确立了紧的1/2最坏情况比率。
AI 中文摘要
我们研究了具有独立私人类型和任意向下封闭可行性约束的双边匹配市场中的贸易收益（GFT）。次优基准是由贝叶斯激励相容、事后个体理性且在每一报告配置下强预算平衡的机制所能实现的最大期望贸易收益。这些约束通常排除了实现最优贸易收益的可能性，并提出了必须损失多少效率的问题。我们证明了在每个这样的匹配市场中，次优贸易收益至少是最优贸易收益的一半。这将Liu等人（2026）最近关于双边贸易的1/2保证推广到了具有多个买方和卖方以及任意向下封闭可行性约束的市场。结合他们在双边贸易中的匹配下界，我们的结果为这类一般匹配市场确立了紧的1/2最坏情况比率。我们的证明基于Brüstle等人（EC 2017）的虚拟贸易收益框架，将问题简化为一参数拉格朗日问题。主要步骤是基于最优边选择区域的几何逐边分析，并结合秩空间中的随机收缩。
英文摘要
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.
Comments34 pages, 1 figure
