提出公平交易的新型收益目标，实现买卖双方利益平衡。
Repeated Bilateral Trade: The Quest for Fairness
- 用非正 Hölder 平均构建从罗尔斯到纳什的公平收益家族。
- 在独立同分布估值下，首次给出全族目标的最优学习率。
- 适合关注平台公平性与机制设计的研究者。
我们从公平性视角研究重复双边交易问题：每轮随机出现买卖双方，平台先设定价格，再根据双方估值决定是否成交。交易仅在双方接受时发生。不同于单纯追求贸易盈余最大化的传统目标，本文关注平台如何实现盈余的均衡分配。研究表明，合理的公平性要求可导出一个一参数的罗尔斯-纳什公平收益族，该族通过非正 Hölder 平均聚合买卖双方净收益。与标准贸易收益和此前研究的罗尔斯公平目标不同，新目标诱导出新的统计结构——期望收益需通过二维奇异核积分恒等式，从阈值反馈中恢复。这带来一个非标准纯探索问题，其自然估计器为带行列依赖和奇异权重的矩形双重求和。假设买卖方估值序列独立同分布且边缘分布未知，我们刻画了整个罗尔斯-纳什族公平收益目标的最优学习速率，给出了匹配的固定置信度样本复杂度与后悔界，精度仅差多对数因子。
原文摘要 · Abstract (English)
We study repeated bilateral trade from a fairness perspective. At each round, a fresh seller-buyer pair arrives, and the platform posts a price before observing the traders' valuations. Trade occurs only if both agents accept the price. Rather than maximizing only the gain from trade, we consider platforms that seek balanced divisions of the generated surplus. We show that natural fairness desiderata lead to a one-parameter Rawls-to-Nash family of fair-gain objectives, obtained by aggregating the seller's and buyer's net gains through nonpositive Hölder means. Unlike the standard gain-from-trade objective and the Rawlsian fair-gain objective studied in prior work, our proposed objectives induce a new statistical structure in which expected rewards are recovered from threshold feedback through a two-dimensional singular-kernel integral identity. This leads to a nonstandard pure-exploration problem whose natural estimators are rectangular double sums with row-column dependence and singular weights. Assuming independent i.i.d. seller and buyer valuation sequences with arbitrary unknown marginals, we characterize the optimal learning rates for the whole Rawls-to-Nash family of fair-gain objectives, giving matching fixed-confidence sample-complexity and regret bounds up to polylogarithmic factors.
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