Improved Revenue Bounds for Posted-Price and Second-Price Mechanisms

TL;DR

This paper introduces improved sequential posted-price mechanisms that outperform previous revenue approximation bounds across various auction settings, including single-unit, multi-unit, and position auctions, by combining simple pricing strategies.

Contribution

It presents a novel SPP mechanism framework that improves approximation factors in multiple auction models, surpassing long-standing benchmarks.

Findings

Better approximation in single-unit settings than previous methods.

First improvement in multi-unit auction approximation in over nine years.

Achieves higher-than-1-1/e approximation in position auctions.

Abstract

We study revenue maximization through sequential posted-price (SPP) mechanisms in single-dimensional settings with $n$ buyers and independent but not necessarily identical value distributions. We construct the SPP mechanisms by considering the best of two simple pricing rules: one that imitates the revenue optimal mchanism, namely the Myersonian mechanism, via the taxation principle and the other that posts a uniform price. Our pricing rules are rather generalizable and yield the first improvement over long-established approximation factors in several settings. We design factor-revealing mathematical programs that crisply capture the approximation factor of our SPP mechanism. In the single-unit setting, our SPP mechanism yields a better approximation factor than the state of the art prior to our work (Azar, Chiplunkar & Kaplan, 2018). In the multi-unit setting, our SPP mechanism yields the first improved approximation factor over the state of the art after over nine years (Yan, 2011 and Chakraborty et al., 2010). Our results on SPP mechanisms immediately imply improved performance guarantees for the equivalent free-order prophet inequality problem. In the position auction setting, our SPP mechanism yields the first higher-than $1-1/e$ approximation factor. In eager second-price (ESP) auctions, our two simple pricing rules lead to the first improved approximation factor that is strictly greater than what is obtained by the SPP mechanism in the single-unit setting.