Revenue Guarantees in Autobidding Platforms

2026-02-16

AI Summary

This study addresses revenue maximization for online advertising platforms under a uniform pricing rule and budget constraints. Focusing on markets with divisible goods and budget-constrained buyers exhibiting linear valuations, the work proposes a pricing and allocation mechanism grounded in First-Price Pacing Equilibrium (FPPE). It establishes, for the first time, that FPPE guarantees at least one-half of the optimal revenue in the offline setting and achieves a 1/4-approximation in the online setting. Furthermore, by formulating the problem via convex optimization and extending it through an Eisenberg–Gale-type program, the analysis is generalized to settings with concave nonlinear valuations, demonstrating robust approximation performance across valuation structures.

Technology Category

• Machine Learning: Online Learning & Bandits
• Search and Optimization: Non-convex Optimization
• Game Theory and Economic Paradigms: Mechanism Design

Application Category

• Economics, Online Markets and Human Computation: Advertising auctions, pricing, markets, and exchanges
• User Modeling, Personalization and Recommendation: User modeling for targeted and personalized online advertising
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web

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.

Problem

• revenue maximization
• autobidding
• budget-constrained buyers
• single-price-per-good
• divisible goods

Innovation

• First-Price Pacing Equilibrium
• Revenue Approximation
• Autobidding
• Convex Programming
• Online Mechanism