Robustly Optimal Mechanisms for Selling Multiple Goods

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 robustlyoptimal selling mechanisms and the worst-case distributions when the ambiguity set satisfies a variety of moment conditions on the values of subsets of goods. We also identify general properties of the ambiguity set that lead to the robust optimality of partial bundling which includes separate sales and pure bundling as special cases.

Costly Multidimensional Screening

“…Significant progress has been made in developing duality approaches to certify optimality of candidate mechanisms Chone 1998, Daskalakis et al 2017;Cai et al 2016, Carroll 2017. In response to the analytical difficulty, several recent papers study either approximately optimal mechanisms (Li and Yao 2013, Babaioff et al 2014, Cai et al 2016, Hart and Nisan 2017, or worst-case optimal mechanisms (Carroll 2017, Koçyiğit et al 2021, Che and Zhong 2021, Deb and Roesler 2021.…”