Revenue Guarantees in Autobidding Platforms

TL;DR

This paper analyzes revenue maximization in autobidding platforms, proving that a specific equilibrium guarantees at least half of the optimal revenue and extending the analysis to online settings and nonlinear valuations.

Contribution

It introduces the FPPE concept for revenue guarantees, proves its effectiveness, and extends the framework to online and nonlinear valuation scenarios.

Findings

FPPE guarantees at least 50% of optimal revenue.

Online FPPE achieves a 1/4-approximation.

Revenue approximation degrades gracefully with valuation nonlinearity.

Abstract

Motivated by autobidding systems in online advertising, we study revenue maximization in markets with divisible goods and budget-constrained buyers with linear valuations. Our aim is to compute a single price for each good and an allocation that maximizes total revenue. We show that the First-Price Pacing Equilibrium (FPPE) guarantees at least half of the optimal revenue, even when compared to the maximal revenue of buyer-specific prices. This guarantee is particularly striking in light of our hardness result: we prove that revenue maximization under individual rationality and single-price-per-good constraints is APX-hard. We further extend our analysis in two directions: first, we introduce an online analogue of FPPE and show that it achieves a constant-factor revenue guarantee, specifically a $1/4$-approximation; second, we consider buyers with concave valuation functions, characterizing an FPPE-type outcome as the solution to an Eisenberg-Gale-style convex program and showing that the revenue approximation degrades gracefully with the degree of nonlinearity of the valuations.