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 au- tobidder behavior. We formalize when model improvements—defined via a refinement relation inspired by filtrations in probability theory—lead to improvements in platform-level Evaluation Cri- teria 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 complete charac- terization 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 auc- tions and budget constraints can break this prop- erty. We provide full numerical counterexamples for all negative results. Our findings have practi- cal implications for advertising platforms seeking to align model improvements with business out- comes.