发表机构
Tilburg University（蒂尔堡大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究针对λ-正则价值分布，探讨基于有限样本的标价定价相对个性化定价的收益比率，发现MHR类中样本均值最优，而一般情形下提出基于顺序统计量的定价规则渐近最优。
AI 中文摘要
个性化定价能最大化市场预期收益，但需要关于个体客户的详细信息。基于潜在价值分布的有限样本，采用简单的标价定价能恢复多少这种收益？我们通过最大化标价定价与个性化定价预期收益之间的最坏情况比率来回答这个问题，该比率针对$\lambda$-正则价值分布这一基本类别。我们的结果揭示了随$\lambda$变化的结构性转变。对于单调风险率（MHR）分布（对应$\lambda=0$），样本均值是最优统计量：整个样本可压缩为其平均值而不损失任何收益。超出MHR类别（对应$\lambda>0$）后，这一性质消失。我们证明样本均值不再最优，表明基于样本的最优定价规则变得相当复杂。尽管如此，我们证明了一种极其简单的基于顺序统计量的定价规则在样本数$n$增长时渐近最优，达到最优近似比，误差紧致为$1/n$阶。我们的分析结合了概率论、逼近论和优化技术，包括双重无限线性规划、超几何函数以及涉及不完全Beta函数的组合恒等式。
英文摘要
Personalised pricing maximises expected revenue from a market but requires detailed information about individual customers. How much of this revenue can be recovered using a simple posted price based on a finite number of samples from the underlying value distribution? We answer this question by maximising the worst-case ratio between the expected revenues of posted and personalised pricing over the fundamental class of $λ$-regular value distributions. Our results reveal a structural transition as a function of $λ$. For the class of monotone hazard rate (MHR) distributions, corresponding to $λ= 0$, the sample mean is an optimal statistic: the entire sample can be compressed into its average without any loss of revenue. Beyond the MHR class, corresponding to $λ> 0$, this property disappears. We show that the sample mean is no longer optimal, revealing that optimal sample-based pricing rules become substantially more intricate. Nevertheless, we show that a remarkably simple order-statistic based pricing rule is asymptotically optimal as the number of samples $n$ grows, achieving the optimal approximation ratio up to a tight error of order $1/n$. Our analysis combines techniques from probability, approximation theory and optimization, including doubly infinite linear programming, hypergeometric functions, and combinatorial identities involving incomplete Beta functions.
CommentsAccepted at the 22nd Conference on Web and Internet Economics (WINE 2026)
