A Simple and Approximately Optimal Mechanism for an Additive Buyer

TL;DR

This paper introduces a simple, computationally feasible mechanism for selling multiple heterogeneous items to a single additive buyer, achieving a constant-factor approximation to the optimal revenue regardless of valuation distributions.

Contribution

It proposes a straightforward mechanism combining separate and bundled pricing that guarantees near-optimal revenue, a first for this complex multi-parameter setting.

Findings

Mechanism achieves constant-factor approximation for any distribution.

First computationally tractable solution for multi-parameter revenue maximization.

Applicable extensions to multiple buyers and correlated valuations.

Abstract

We consider a monopolist seller with $n$ heterogeneous items, facing a single buyer. The buyer has a value for each item drawn independently according to (non-identical) distributions, and her value for a set of items is additive. The seller aims to maximize his revenue. We suggest using the a-priori better of two simple pricing methods: selling the items separately, each at its optimal price, and bundling together, in which the entire set of items is sold as one bundle at its optimal price. We show that for any distribution, this mechanism achieves a constant-factor approximation to the optimal revenue. Beyond its simplicity, this is the first computationally tractable mechanism to obtain a constant-factor approximation for this multi-parameter problem. We additionally discuss extensions to multiple buyers and to valuations that are correlated across items.