A Note on Approximate Revenue Maximization with Two Items

TL;DR

This paper investigates revenue maximization for selling two items to a single buyer, providing tighter bounds on revenue when items have different individual revenues, building on prior work by Hart and Nisan.

Contribution

It improves the existing revenue bounds for two-item sales by considering cases where items have different separate revenues.

Findings

Tighter revenue bounds for two-item sales with different individual revenues.

Extension of Hart and Nisan's result to more general cases.

Insights into optimal selling strategies for two items.

Abstract

We consider the problem of maximizing revenue when selling 2 items to a single buyer with known valuation distributions. Hart and Nisan showed that selling each item separately using the optimal Myerson's price, gains at least half of the revenue attainable by optimal auction for two items. We show that in case the items have different revenues when sold separately the bound can be tightened.