Selling a single item to $n$ self-interested buyers is a fundamental problem in economics, where the two objectives typically considered are welfare maximization and revenue maximization. Since the optimal mechanisms are often impractical and do not work for sequential buyers, posted pricing mechanisms, where fixed prices are set for the item for different buyers, have emerged as a practical and effective alternative. This paper investigates how many samples are needed from buyers' value distributions to find near-optimal posted prices, considering both independent and correlated buyer distributions, and welfare versus revenue maximization. We obtain matching upper and lower bounds (up to logarithmic factors) on the sample complexity for all these settings.

翻译：向$n$个自利买家销售单件商品是经济学中的一个基本问题，通常考虑的两个目标分别是社会福利最大化和收益最大化。由于最优机制往往不切实际且不适用于序贯买家，为不同买家设定固定价格的定价机制已成为一种实用而有效的替代方案。本文研究了在考虑买家价值分布独立与相关的情形下，以及社会福利最大化与收益最大化的不同目标时，需要从买家价值分布中获取多少样本才能找到近似最优的定价。我们针对所有这些设定，获得了样本复杂度的匹配上界与下界（相差对数因子以内）。