Autobidding Equilibria in Sponsored Shopping

2026-02-25

AI Summary

This study addresses the existence and efficiency of equilibria in combinatorial ad auctions for ROI-constrained autobidders in digital markets, focusing on Sponsored Shopping scenarios where advertisers employ uniform bidding strategies to maximize value. Leveraging game theory and mechanism design, combined with models of autobidding, ROI-constrained optimization, and combinatorial auction analysis, the work establishes—for the first time—the existence of autobidding equilibria under both Generalized Second-Price (GSP) and Vickrey–Clarke–Groves (VCG) mechanisms. Furthermore, it rigorously proves a tight upper bound of 2 on the welfare loss relative to the optimal allocation, i.e., a price of anarchy (PoA) of at most 2. These results confirm the pervasive existence of equilibria under realistic bidding constraints and provide strong theoretical guarantees for platform mechanism design in complex advertising environments.

Technology Category

• Game Theory and Economic Paradigms: Mechanism Design
• Multiagent Systems: Mechanism Design
• Search and Optimization: Adversarial Search

Application Category

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

Abstract

As commerce shifts to digital marketplaces, platforms increasingly monetize traffic through Sponsored Shopping auctions. Unlike classic ``Sponsored Search", where an advertiser typically bids for a single link, these settings involve advertisers with broad catalogs of distinct products. In these auctions, a single advertiser can secure multiple slots simultaneously to promote different items within the same query. This creates a fundamental complexity: the allocation is combinatorial, as advertisers simultaneously win a bundle of slots rather than a single position. We study this setting through the lens of autobidding, where value-maximizing agents employ uniform bidding strategies to optimize total value subject to Return-on-Investment (ROI) constraints. We analyze two prevalent auction formats: Generalized Second-Price (GSP) and Vickrey-Clarke-Groves (VCG). Our first main contribution is establishing the universal existence of an Autobidding Equilibrium for both settings. Second, we prove a tight Price of Anarchy (PoA) of 2 for both mechanisms.

Problem

• Sponsored Shopping
• Autobidding
• Combinatorial Auctions
• ROI Constraints
• Equilibrium

Innovation

• Autobidding Equilibrium
• Sponsored Shopping
• Combinatorial Allocation
• Price of Anarchy
• ROI Constraints