Problem definition: We study a data-driven pricing problem in which a seller sets a price for a single item based on demand observed at a limited number of historical prices. Our goal is to quantify the value of such information and to guide efficient price experimentation under practical constraints. Methodology/results: Our main methodological contribution is an exact reduction that characterizes the maximin revenue ratio, defined as the worst-case revenue achievable using only past data relative to the optimal revenue under full information. This reduction transforms an infinite-dimensional problem into a tractable one-dimensional optimization problem, allowing us to compute near-optimal pricing policies with explicit guarantees and to precisely quantify the value of historical data. Managerial implications: Motivated by practical constraints that limit price changes, we first evaluate the value of local information and show that the sign of the revenue gradient at a single price can provide significant guidance. We then use our framework to design efficient price experiments: we develop a method to select the next price to test so as to maximize future robust performance, and show how to substantially reduce the number of experiments needed to achieve target revenue guarantees in dynamic pricing. Finally, we show that our approach remains effective with noisy demand data, achieving near-optimal performance with as few as 25 to 100 samples per price.

翻译：问题定义：我们研究一个数据驱动的定价问题，卖家依据在有限历史价格点观察到的需求为单一品项设定价格，目标是量化此类信息的价值，并在实际约束下指导高效的定价实验。方法论/结果：我们的主要方法论贡献是一种精确的降维方法，该降维刻画了最大最小收益比，即仅利用历史数据可实现的在最坏情况下收益相对于完全信息下最优收益的比值。这一降维将无限维问题转化为易处理的一维优化问题，使我们能够计算具有显式保证的近似最优定价策略，并精确量化历史数据的价值。管理启示：在限制价格变动的实际约束驱动下，我们首先评估局部信息的价值，表明单一价格点上收益梯度的符号能提供重要指导。随后，我们利用该框架设计高效的定价实验：开发了一种方法选择下一个测试的价格点，以最大化未来的稳健性能，并展示了在动态定价中如何显著减少达到目标收益保证所需的实验次数。最后，我们证明该方法在含噪声的需求数据下依然有效，在每价格点仅需25至100个样本时即可实现接近最优的性能。