The Power of Simple Menus in Robust Selling Mechanisms

• 成果类型: Article
• 署名作者: Wang, Shixin
• 署名单位: Chinese University of Hong Kong
• 刊物名称: MANAGEMENT SCIENCE
• ISSN/ISSBN: 0025-1909
• DOI: 10.1287/mnsc.2023.03738
• 发表日期: 2025
• 关键词: Robust pricing; robust screening; minimax regret; competitive ratio; simple menu

摘要

We study a robust selling problem where a seller attempts to sell one item to a buyer but is uncertain about the buyer's valuation distribution. The existing literature shows that robust screening provides a stronger theoretical guarantee than robust deterministic pricing but at the expense of implementation complexity as it requires a menu of infinite options. Our research aims to find simple mechanisms to hedge against market ambiguity effectively. We develop a general framework for robust selling mechanisms with a finite menu (or randomization across finite prices). We propose a tractable reformulation that addresses various ambiguity sets of the buyer's valuation distribution, including support, mean, and quantile ambiguity sets. We derive optimal selling mechanisms and corresponding performance ratios for different menu sizes, which show that even a modest menu size can deliver benefits similar to those achieved by the optimal robust mechanism with infinite options, establishing a favorable trade-off between theoretical performance and implementation simplicity. Remarkably, a menu size of merely two can significantly enhance the performance ratio compared with deterministic pricing.