{"ID":22952682,"CreatedAt":"2026-09-17T02:12:05.498442134Z","UpdatedAt":"2026-09-20T18:11:56.143995915Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2609.18724","arxiv_id":"2609.18724","title":"Second-Best Gains from Trade in Matching Markets","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.","short_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 balance...","url_abs":"https://arxiv.org/abs/2609.18724","url_pdf":"https://arxiv.org/pdf/2609.18724v1","authors":"[\"Xiaohui Bei\",\"Bo Li\",\"Wenhao Wu\",\"Shengwei Zhou\"]","published":"2026-09-16T14:26:07Z","proceeding":"cs.GT","tasks":"[\"cs.GT\"]","methods":"[]","has_code":false}