Autobidding Equilibria in Sponsored Shopping

TL;DR

This paper investigates autobidding in sponsored shopping auctions with multiple slots and products, establishing equilibrium existence and analyzing efficiency loss through Price of Anarchy.

Contribution

It introduces the first analysis of autobidding equilibria in combinatorial sponsored shopping auctions, proving their existence and quantifying efficiency loss.

Findings

Existence of autobidding equilibrium in GSP and VCG auctions.

Price of Anarchy is tightly bounded at 2 for both auction formats.

Provides insights into the strategic behavior of value-maximizing autobidders.

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.