Improved Two Sample Revenue Guarantees via Mixed-Integer Linear Programming

TL;DR

This paper analyzes the Empirical Revenue Maximizing (ERM) mechanism with two samples, providing improved revenue guarantees through mixed-integer linear programming, narrowing the bounds of its worst-case performance.

Contribution

The paper introduces MILP-based methods to derive tighter revenue guarantees for ERM with two samples, improving upon previous bounds.

Findings

ERM guarantees at least 0.5914 of optimal revenue

Worst-case efficiency is at most 0.61035 of optimal revenue

Improves previous bounds of 0.558 and 0.642

Abstract

We study the performance of the Empirical Revenue Maximizing (ERM) mechanism in a single-item, single-seller, single-buyer setting. We assume the buyer's valuation is drawn from a regular distribution $F$ and that the seller has access to {\em two} independently drawn samples from $F$. By solving a family of mixed-integer linear programs (MILPs), the ERM mechanism is proven to guarantee at least $.5914$ times the optimal revenue in expectation. Using solutions to these MILPs, we also show that the worst-case efficiency of the ERM mechanism is at most $.61035$ times the optimal revenue. These guarantees improve upon the best known lower and upper bounds of $.558$ and $.642$, respectively, of [Daskalakis & Zampetakis, '20].