The Power of Simple Menus in Robust Selling Mechanisms
研究卖家在不确定买家估值分布时，使用有限选项菜单（如仅两个选项）的简单机制，能否在保证理论性能的同时简化实施，发现小菜单即可接近无限选项的最优稳健机制效果。
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. This paper was accepted by Chung Piaw Teo, optimization and decision analytics. Funding: This research was supported by the National Natural Science Foundation of China [Grant 72394395]. Supplemental Material: The online appendix is available at https://doi.org/10.1287/mnsc.2023.03738 .