Vulnerabilities of Single-Round Incentive Compatibility in Auto-bidding: Theory and Evidence from ROI-Constrained Online Advertising Markets
Juncheng Li, Pingzhong Tang
TL;DR
The paper addresses ROI-constrained auto-bidding markets where platforms control bidding agents and run simultaneous auctions. It develops an auto-bidding equilibrium framework to capture steady-state market behavior under multiplicative pacing and analyzes the computational and practical consequences, revealing $PPAD$-hardness for equilibrium computation and $APX$-hardness for revenue/welfare optimization. It uncovers non-monotonicity and utility instability, demonstrates interference in A/B testing, and argues that first-price auctions can outperform second-price in this context, explaining industry shifts (e.g., Google's partial switch). The findings highlight the limitations of relying on traditional IC results in real-world auto-bidding markets and emphasize the need to consider sub-market structure and practical testing biases for robust auction design. Overall, the work provides both theoretical hardness results and actionable insights for practitioners designing and evaluating auto-bidding-enabled ad markets.
Abstract
Most of the work in the auction design literature assumes that bidders behave rationally based on the information available for every individual auction, and the revelation principle enables designers to restrict their efforts to incentive compatible (IC) mechanisms. 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 platform, and an advertiser can only participate by setting performance objectives and constraints for its proxy auto-bidder provided by the platform. The prevalence of auto-bidding necessitates a review of auction theory. In this paper, we examine the markets through the lens of ROI-constrained value-maximizing campaigns. We show that second price auction exhibits many undesirable properties (computational hardness, non-monotonicity, instability of bidders' utilities, and interference in A/B testing) and loses its dominant theoretical advantages in single-item scenarios. In addition, we make it clear how IC and its runner-up-winner interdependence contribute to each property. We hope that our work could bring new perspectives to the community and benefit practitioners to attain a better grasp of real-world markets.