Auto-bidding Equilibrium in ROI-Constrained Online Advertising Markets

Most of the work in auction design literature assumes that bidders behave rationally based on the information available for each individual auction. However, in today's online advertising markets, one of the most important real-life applications of auction design, the data and computational power required to bid optimally are only available to the auction designer, and an advertiser can only participate by setting performance objectives (clicks, conversions, etc.) for the campaign. In this paper, we focus on value-maximizing campaigns with return-on-investment (ROI) constraints, which is widely adopted in many global-scale auto-bidding platforms. Through theoretical analysis and empirical experiments on both synthetic and realistic data, we find that second price auction exhibits many undesirable properties and loses its dominant theoretical advantages in single-item scenarios. In particular, second price auction brings equilibrium multiplicity, non-monotonicity, vulnerability to exploitation by both bidders and even auctioneers, and PPAD-hardness for the system to reach a steady-state. We also explore the broader impacts of the auto-bidding mechanism beyond efficiency and strategyproofness. In particular, the multiplicity of equilibria and the input sensitivity make advertisers' utilities unstable. In addition, the interference among both bidders and advertising slots introduces bias into A/B testing, which hinders the development of even non-bidding components of the platform. The aforementioned phenomena have been widely observed in practice, and our results indicate that one of the reasons might be intrinsic to the underlying auto-bidding mechanism. To deal with these challenges, we provide suggestions and candidate solutions for practitioners.