Model Monotonicity in Autobidding Auctions: When Do Better Predictions Lead to Better Outcomes?

Online advertising platforms rely on machine learning models to predict click-through rates (pCTR) and conversion rates (pCVR) for auction mechanisms. We introduce a novel framework to study the interaction between recommender system model quality, auction format, and autobidder behavior. We formalize when model improvements---defined via a refinement relation inspired by filtrations in probability theory---lead to improvements in platform-level Evaluation Criteria Metrics (ECM) such as revenue, welfare, or liquid welfare. Our main contributions are: (1) a formal definition of model improvement based on cluster refinement, and (2) a systematic characterization of ECM monotonicity across different combinations of bidder types (tCPA, max-CPA), auction formats (first-price, second-price, VCG), and budget constraints. We show that first-price auctions with uniform bidding guarantee revenue monotonicity for tCPA bidders without budgets (via Jensen's inequality), while second-price auctions and budget constraints can break this property. We provide full numerical constructions for the non-monotonicity results. Our findings have practical implications for advertising platforms seeking to align model improvements with business outcomes.

Online advertising platforms use machine learning to predict which ads people are likely to click on or act on. These predictions are then used by automated systems that decide which advertiser wins a chance to show an ad and how much they pay. It is natural to expect that better predictions should always improve outcomes, such as higher platform revenue or better matches between advertisers and users. This paper shows that this is not always true. When a prediction system becomes more detailed, advertisers may change how they bid. In some cases this helps, but in other cases it can reduce competition, shift ads toward different advertisers, or interact badly with spending limits. We develop a mathematical framework for studying when more detailed prediction models lead to better outcomes in online advertising systems. We identify the settings where improvements are guaranteed and give examples where better predictions can unexpectedly make revenue or overall value worse. The main takeaway is that platforms should evaluate model improvements at the full system level, not just by checking whether the prediction model itself is more accurate.