从下游价格中学习：具有揭示定价最优性的稳健上游决策

中文摘要 AI 辅助

问题定义：上游企业常观察下游合作伙伴的零售价格和销售情况，但不知驱动这些决策的消费者估值分布，传统需求分析将零售价格视为协变量。我们研究上游企业如何利用观察到的价格是最优选择这一事实，特别是在交易历史稀疏时。方法/结果：在常规消费者估值下，下游零售商的最优价格除了揭示该价格下的需求分位数外，还揭示了虚拟价值条件。我们利用这些信号构建形状受限的模糊集，其可行局部族是标量区间。我们表明最坏情况局部模型在端点处达到，将连续分布问题简化为双场景稳健报童问题。我们还刻画了揭示最优性如何收紧仅分位数基准以及有界决策误差如何削弱这一优势。在六个常规估值模型中实验，三（五）个历史记录将平均神谕利润比从0.892提高到0.955（0.918提高到0.986）；端点法与1001点模糊网格匹配且快700多倍。管理启示：下游价格应视为战略决策数据而非仅需求协变量。该框架使上游企业能将少量定价记录转化为可处理的决策规则，当下游决策不可靠时提供仅分位数信息的原则性退路。

英文摘要

Upstream suppliers often set wholesale prices and reserve capacity without direct access to the detailed demand information held by downstream retailers. We study how a supplier can learn from a short history of wholesale prices, the retail prices subsequently chosen by a better-informed retailer, and the associated purchase probabilities. A quantile-only method (Q) uses each retail price and purchase probability as a demand observation. Our decision-informed method (DI) also uses the wholesale price under which the retailer chose that price. This additional context rules out demand curves that fit the observed sales outcomes but cannot explain the retailer's past choices. We characterize the worst-case retailer response to a new wholesale price under a broad, nonparametric class of demand curves. When the retailer has a unique best price, the relevant uncertainty is summarized by the lowest demand that remains possible. When several prices are tied, the supplier instead evaluates a finite collection of induced-demand cases. We also distinguish two forms of imperfect behavior. Under condition error (CE), the observed price is retained but its link to the wholesale price may be imperfect. Under price error (PE), the observed price may lie near an unobserved exact optimum. Both extensions remain computationally finite. The resulting downstream-demand summary leads directly to robust wholesale-pricing and stocking decisions. Numerical experiments across six demand environments show that DI provides substantial value with only a few transactions and remains useful under moderate error; with three observations and $α=0$, DI improves the profit-to-oracle ratio by 9.1--11.8 percentage points.

发表机构

• School of Management and Engineering, Nanjing University（南京大学工程管理学院）

机构由 AI 辅助整理，请以论文原文为准。