Approximate Revenue Maximization with Multiple Items

TL;DR

This paper analyzes simple selling mechanisms for multiple items, showing they guarantee a significant fraction of the optimal revenue under various independence and distribution assumptions, and extends results to multiple buyers.

Contribution

It provides approximation guarantees for simple mechanisms like selling separately or bundling in multi-item revenue maximization, including for multiple buyers.

Findings

Selling separately guarantees at least 73% of optimal revenue for two i.i.d. goods.

For k independent goods, selling separately guarantees at least c/log^2 k of optimal revenue.

Bundling guarantees at least c/log k of optimal revenue for i.i.d. goods.

Abstract

Maximizing the revenue from selling _more than one_ good (or item) to a single buyer is a notoriously difficult problem, in stark contrast to the one-good case. For two goods, we show that simple "one-dimensional" mechanisms, such as selling the goods separately, _guarantee_ at least 73% of the optimal revenue when the valuations of the two goods are independent and identically distributed, and at least $50\%$ when they are independent. For the case of $k>2$ independent goods, we show that selling them separately guarantees at least a $c/\log^2 k$ fraction of the optimal revenue; and, for independent and identically distributed goods, we show that selling them as one bundle guarantees at least a $c/\log k$ fraction of the optimal revenue. Additional results compare the revenues from the two simple mechanisms of selling the goods separately and bundled, identify situations where bundling is optimal, and extend the analysis to multiple buyers.