A Field Guide to Personalized Reserve Prices

TL;DR

This paper compares lazy and eager reserve price strategies in non-identical bidder auctions, revealing their differences in optimization, welfare, and revenue, with practical implications supported by real-world data simulations.

Contribution

It introduces a comprehensive analysis of lazy versus eager reserve prices, highlighting their properties, optimization challenges, and revenue implications in auctions with heterogeneous bidders.

Findings

Lazy reserves are easier to optimize and test in production.

Eager reserves lead to higher welfare but are NP-complete to optimize.

Overall revenue is within a factor of 2 between the two methods.

Abstract

We study the question of setting and testing reserve prices in single item auctions when the bidders are not identical. At a high level, there are two generalizations of the standard second price auction: in the lazy version we first determine the winner, and then apply reserve prices; in the eager version we first discard the bidders not meeting their reserves, and then determine the winner among the rest. We show that the two versions have dramatically different properties: lazy reserves are easy to optimize, and A/B test in production, whereas eager reserves always lead to higher welfare, but their optimization is NP-complete, and naive A/B testing will lead to incorrect conclusions. Despite their different characteristics, we show that the overall revenue for the two scenarios is always within a factor of 2 of each other, even in the presence of correlated bids. Moreover, we prove that the eager auction dominates the lazy auction on revenue whenever the bidders are independent or symmetric. We complement our theoretical results with simulations on real world data that show that even suboptimally set eager reserve prices are preferred from a revenue standpoint.