发表机构
School of Physical and Mathematical Sciences, Nanyang Technological University（南洋理工大学物理与数学科学学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
研究双边匹配市场中简单机制对贸易收益的近似，证明广义随机报价者机制的最坏情况近似比为紧致的$e$，改进了先前结果，并确立其最优性。
AI 中文摘要
我们研究在具有独立买方价值和卖方成本的双边匹配市场中，简单机制如何近似贸易收益（GFT），其中可行结果构成任意向下封闭的匹配族。该模型将双边贸易和双重拍卖作为特例。我们关注广义随机报价者（GRO）机制，它是广义卖方报价机制（GSOM）和广义买方报价机制（GBOM）的等量混合。我们确定了GRO相对于最优GFT的精确最坏情况近似比，证明其为$e$。这改进了同一机制的先前$3.15$近似保证（Babaioff等，STOC 2026）。在双边贸易中，该结果意味着随机报价者机制具有$1/e$保证，改进了先前的$1/\pi$界（Jo 2026）。我们的分析使用分位数空间中的二维不等式来比较最优GFT与最优单边拍卖利润。对于每笔潜在交易，我们识别最优分配选择该交易的买方价值和卖方成本区域，然后在分位数空间中随机收缩该区域，产生预期利润可精确评估的标价规则。我们通过构造具有正则类型分布、两两不相交的交易边和单一背包约束的市场来确立$e$近似的紧致性。在这些实例上，GRO的预期GFT接近最优GFT的$1/e$比例，因此即使在这些限制下也排除了任何更好的保证。
英文摘要
We study how well simple mechanisms approximate gains from trade (GFT) in two-sided matching markets with independent buyer values and seller costs, where feasible outcomes form an arbitrary downward-closed family of matchings. This model includes bilateral trade and double auctions as special cases. We focus on the Generalized Random-Offerer (GRO) mechanism, which is an equal mixture of the Generalized Sellers-Offering Mechanism (GSOM) and the Generalized Buyers-Offering Mechanism (GBOM). We determine GRO's exact worst-case approximation ratio with respect to first-best GFT, showing that it is $e$. This improves the previous $3.15$ approximation guarantee (Babaioff et al. STOC 2026) for the same mechanism. In bilateral trade, the result implies a $1/e$ guarantee for the random-offerer mechanism, improving the previous $1/π$ bound (Jo 2026). Our analysis uses a two-dimensional inequality in quantile space to compare first-best GFT with optimal one-sided auction profits. For each potential trade, we identify the region of buyer values and seller costs for which the first-best allocation selects that trade, and then randomly shrink this region in quantile space, yielding posted-price rules whose expected profits can be evaluated exactly. We establish tightness of the $e$ approximation by constructing markets with regular type distributions, pairwise disjoint trading edges, and a single knapsack constraint. On these instances, GRO's expected GFT approaches a $1/e$ fraction of first-best GFT, therefore ruling out any better guarantee even under these restrictions.
