The Power of Simple Menus in Robust Selling Mechanisms

TL;DR

This paper develops simple, finite-menu selling mechanisms that effectively hedge against market ambiguity, achieving near-optimal performance with minimal complexity compared to infinite-menu robust screening.

Contribution

It introduces a tractable framework for robust selling with finite menus, demonstrating that small menus can approximate the performance of complex infinite-menu mechanisms.

Findings

Two-menu mechanisms significantly improve performance ratios.

Finite menus can closely approximate infinite-menu robustness.

A simple menu size of two offers substantial benefits over deterministic pricing.

Abstract

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. 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, showing 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 to deterministic pricing.