Autobidding Equilibria in Sponsored Shopping

A team of computer scientists including Paul Dütting and Renato Paes Leme has published a foundational paper titled 'Autobidding Equilibria in Sponsored Shopping' on arXiv, addressing the complex game theory of modern digital marketplaces. Unlike traditional sponsored search where advertisers bid for a single link, sponsored shopping involves advertisers with broad product catalogs competing for multiple slots simultaneously within a single query. This creates a combinatorial allocation problem where value-maximizing agents use uniform bidding strategies subject to ROI constraints. The researchers analyze this through the lens of autobidding, examining two dominant auction formats: Generalized Second-Price (GSP) and Vickrey-Clarke-Groves (VCG).

The paper's first major contribution establishes the universal existence of an Autobidding Equilibrium for both GSP and VCG mechanisms in sponsored shopping settings. Their second key result proves a tight Price of Anarchy (PoA) bound of 2 for both auction formats, meaning the worst-case efficiency loss compared to an optimal allocation is at most a factor of two. This theoretical guarantee provides crucial stability and performance bounds for platforms like Amazon, Google Shopping, and other e-commerce marketplaces that rely on these auction mechanisms. The findings give platform designers confidence that automated bidding systems will converge to predictable equilibria while maintaining reasonable economic efficiency, fundamentally advancing our understanding of multi-slot advertising auctions in combinatorial environments.