Robustly Optimal Mechanisms for Selling Multiple Goods

TL;DR

This paper characterizes the structure of revenue-maximizing selling mechanisms for multiple goods under worst-case valuation distributions, revealing conditions that justify bundling strategies like separate sales and pure bundling.

Contribution

It provides a precise characterization of robustly optimal mechanisms and worst-case distributions under various moment-based ambiguity sets.

Findings

Categorical bundling is justified by ambiguity set properties.

Explicit forms of robustly optimal mechanisms are identified.

Worst-case distributions are characterized for different ambiguity conditions.

Abstract

We study robustly optimal mechanisms for selling multiple items. The seller maximizes revenue against a worst-case distribution of a buyer's valuations within a set of distributions, called an "ambiguity" set. We identify the exact forms of robustly optimal selling mechanisms and the worst-case distributions when the ambiguity set satisfies various moment conditions on the values of subsets of goods. The analysis reveals general properties of the ambiguity set that justifies categorical bundling, which includes separate sales and pure bundling as special cases.