We investigate online pricing in two-sided markets where a platform repeatedly posts prices based on binary accept/reject feedback to maximize gains-from-trade (GFT) or profit. We characterize the regret achievable across three mechanism classes: Single-Price, Two-Price, and Segmented-Price. For profit maximization, we design an algorithm using Two-Price Mechanisms that achieves $O(n^2 \log\log T)$ regret, where $n$ is the number of traders. For GFT maximization, the optimal regret depends critically on both market size and mechanism expressiveness. Constant regret is achievable in bilateral trade, but this guarantee breaks down as the market grows: even in a one-seller, two-buyer market, any algorithm using Single-Price Mechanisms suffers regret at least $Ω\!\big(\frac{\log\log T}{\log\log\log\log T}\big)$, and we provide a nearly matching $O(\log\log T)$ upper bound for general one-to-many markets. In full many-to-many markets, we prove that Two-Price Mechanisms inevitably incur linear regret $Ω(T)$ due to a \emph{mismatch phenomenon}, wherein inefficient pairings prevent near-optimal trade. To overcome this barrier, we introduce \emph{Segmented-Price Mechanisms}, which partition traders into groups and assign distinct prices per group. Using this richer mechanism, we design an algorithm achieving $O(n^2 \log\log T + n^3)$ regret for GFT maximization. Finally, we extend our results to the contextual setting, where traders' costs and values depend linearly on observed $d$-dimensional features that vary across rounds, obtaining regret bounds of $O(n^2 d \log\log T + n^2 d \log d)$ for profit and $O(n^2 d^2 \log T)$ for GFT. Our work delineates sharp boundaries between learnable and unlearnable regimes in two-sided dynamic pricing and demonstrates how modest increases in pricing expressiveness can circumvent fundamental hardness barriers.

翻译：本文研究双边市场中的在线定价问题，平台基于二元接受/拒绝反馈重复发布价格，以最大化交易收益（GFT）或利润。我们刻画了三种机制类别（单一价格、双重价格和分段价格）可实现的遗憾界。针对利润最大化，我们设计了一种采用双重价格机制的算法，实现了$O(n^2 \log\log T)$的遗憾，其中$n$为交易者数量。对于GFT最大化，最优遗憾关键取决于市场规模与机制表达能力。在双边交易中可实现常数遗憾，但随着市场扩大该保证不再成立：即使在单一卖方、两个买方的市场中，任何采用单一价格机制的算法至少遭受$Ω\!\big(\frac{\log\log T}{\log\log\log\log T}\big)$的遗憾，我们针对一般一对多市场给出了近乎匹配的$O(\log\log T)$上界。在完整的多对多市场中，我们证明双重价格机制由于存在\emph{错配现象}（低效配对阻碍近最优交易）必然产生线性遗憾$Ω(T)$。为突破此障碍，我们提出\emph{分段价格机制}，将交易者分组并为每组分配不同价格。基于这一更丰富的机制，我们设计了实现$O(n^2 \log\log T + n^3)$遗憾的GFT最大化算法。最后，我们将结果扩展至情境化场景，其中交易者的成本与价值线性依赖于每轮变化的$d$维可观测特征，获得了利润$O(n^2 d \log\log T + n^2 d \log d)$与GFT$O(n^2 d^2 \log T)$的遗憾界。本研究清晰划定了双边动态定价中可学习与不可学习机制的边界，并证明了适度增强定价表达能力如何能规避根本性的计算困难壁垒。