Mechanism Design for Subadditive Agents via an Ex-Ante Relaxation

TL;DR

This paper introduces a simple, sequential two-part tariff mechanism that approximates optimal revenue in a multi-buyer setting with subadditive values, expanding the scope of prior models to more complex, heterogeneous buyer constraints.

Contribution

It develops a unified, simple mechanism for multi-buyer revenue maximization with subadditive values, extending prior work from special cases to more general, heterogeneous buyer constraints.

Findings

Achieves a constant factor approximation to optimal revenue.

Extends ex ante relaxation techniques to subadditive valuation settings.

Provides a unified approach for diverse buyer constraints.

Abstract

We consider the problem of maximizing revenue for a monopolist offering multiple items to multiple heterogeneous buyers. We develop a simple mechanism that obtains a constant factor approximation under the assumption that the buyers' values are additive subject to a feasibility constraint and independent across items. Importantly, different buyers in our setting can have different constraints on the sets of items they desire. Our mechanism is a sequential variant of two-part tariffs. Prior to our work, simple approximation mechanisms for such multi-buyer problems were known only for the special cases of all unit-demand or all additive value buyers. Our work expands upon and unifies long lines of work on unit-demand settings and additive settings. We employ the ex ante relaxation approach developed by Alaei (2011) for reducing a multiple-buyer mechanism design problem with an ex post supply constraint into single-buyer ones with ex ante supply constraints. Solving the single-agent problems requires us to significantly extend techniques developed in the context of additive values by Li and Yao (2013) and their extension to subadditive values by Rubinstein and Weinberg (2015).