We study prior-independent pricing for selling a single item to a single buyer when the seller observes only a single sample from the valuation distribution, while the buyer knows the distribution. Classical robust pricing approaches either rely on distributional statistics, which typically require many samples to estimate, or directly use revealed samples to determine prices and allocations. We show that these two regimes can be bridged by leveraging the buyer's informational advantage: pricing policies that conventionally require the seller to know statistics such as the mean, $L^η$-norm, or superquantile can, in our framework, be implemented using only a single hidden sample. We introduce hidden pricing mechanisms, in which the seller commits ex ante to a pricing rule based on a single sample that is revealed only after the buyer's participation decision. We show that every concave pricing policy can be implemented in this way. To evaluate performance guarantees, we develop a general reduction for analyzing monotone pricing policies over $α$-regular distributions, enabling a tractable characterization of worst-case instances. Using this reduction, we characterize the optimal monotone hidden pricing mechanisms and compute their approximation ratios; in particular, we obtain an approximation ratio of approximately $0.79$ for monotone hazard rate (MHR) distributions. We further establish impossibility results for general concave pricing policies and for all prior-independent mechanisms. Finally, we show that our framework also applies to statistic-based robust pricing, thereby unifying sample-based and statistic-based approaches.

翻译：本文研究在卖方仅能观察到估值分布的一个样本而买方知晓完整分布的情况下，销售单件商品的先验无关定价问题。经典的鲁棒定价方法通常依赖于需要大量样本估计的分布统计量，或直接利用已观测样本确定价格与分配方案。我们证明，通过利用买方的信息优势，可以桥接这两种范式：传统上需要卖方掌握均值、$L^η$范数或超分位数等统计量的定价策略，在我们的框架下仅需一个隐藏样本即可实现。我们提出隐藏定价机制——卖方事前承诺基于单个样本的定价规则，而该样本仅在买方参与决策后公开。我们证明所有凹性定价策略均可通过此方式实现。为评估性能保证，我们建立了分析$α$-正则分布上单调定价策略的通用约简方法，从而实现对最坏案例的可处理刻画。利用该约简，我们刻画了最优单调隐藏定价机制并计算其近似比；特别地，对于单调失效率（MHR）分布，我们获得了约$0.79$的近似比。我们进一步建立了针对一般凹性定价策略及所有先验无关机制的不可能性结果。最后，我们证明该框架同样适用于基于统计量的鲁棒定价，从而统一了基于样本与基于统计量的方法。