Towards Efficient Auction Design with ROI Constraints

Xinyu Tang, Hongtao Lv, Yingjie Gao, Fan Wu, Lei Liu, Lizhen Cui

Abstract: Online advertising stands as a significant revenue source of the Internet. Recently, the trend among advertisers tilting towards the use of auto-bidding tools has heralded the emergence of a new model of bidders operating with constraints related to return on investment (ROI). However, most of the current research on ROI-constrained bidders in auction design only focuses on either the ROI constraints or values of bidders being private, while it is more practical to keep them both private in reality. Designing a truthful mechanism for bidders with both private values and ROI constraints introduces complexities because of the characteristics of designing mechanisms with multiple parameters. To remedy this, we divide bidders into binary classes: the traditional utility maximizers (UMs) who can be viewed as having an ROI constraint of 1, and the ROI-constrained bidders (RBs) who share a fixed ROI constraint denoted as γ. This framework retains the essence of multi-parameter mechanism design but transitions this into a more tractable form. Then we introduce a novel auction mechanism, cleverly combining the conventional VCG mechanism and an existing mechanism for public ROI-constrained bidders which is called Cavallo's mechanism. Our mechanism can achieve an approximation ratio of 3 over 2 on social welfare. Additionally, we unearth new insights into the limitations posed by ROI constraints. When the ROI constraint γ exceeds 2, the lower bound of social welfare is 5 over 4; when it falls below 2, the lower bound becomes 3+γ over 2+3γ-γ2.