A Note on the Ratio of Revenues Between Selling in a Bundle and Separately

TL;DR

This paper analyzes revenue maximization strategies for selling multiple items to a single buyer, demonstrating that bundling can achieve at least 55.9% of the revenue compared to separate sales, and this bound is tight.

Contribution

It establishes a lower bound on the revenue ratio between bundling and separate sales for i.i.d. valuations, showing the bound is attainable.

Findings

Bundling yields at least 55.9% of the revenue of separate sales.

The 55.9% revenue ratio bound is tight and achievable.

The analysis applies to i.i.d. valuation distributions for the items.

Abstract

We consider the problem of maximizing revenue when selling k items to a single buyer with known valuation distributions. We show that for a single, additive buyer whose valuations for for the items are distributed according to i.i.d. distributions which are known to the seller, the ratio of revenue from selling in a bundle to selling separately is at least 55.9% and this gap is attainable.