Efficiency of Proportional Mechanisms in Online Auto-Bidding Advertising

Real-time bidding is central to computational advertising, comprising three elements: Supply Side Platform (SSP) selling ad impressions, Demand Side Platform (DSP) bidding for advertisers, and Ad Exchange conducting auctions between them. Traditional auto-bidding algorithms focus solely on the DSP side, maximizing advertiser conversions by adjusting bids against competitors. However, current big ad platforms, such as social media and e-commerce companies, now integrate SSP, DSP, and Ad Exchange functions internally. From such ad platforms' perspective, the goal of the auto-bidding algorithms is not only to maximize the advertisers' conversions, but also the total revenue of the platform. Given the lack of platform-centric evaluation frameworks and the pressing need to advance auto-bidding research, we propose PlatformBid - the first comprehensive benchmark designed from a unified ad platform's perspective. To accurately reflect the real-world auto-bidding scenarios, we define three representative settings: (1) homogeneous competition with identical algorithms across advertisers, (2) heterogeneous competition with diverse algorithmic strategies, and (3) promotional competition where some advertisers surge budgets for boosting sales during promotional events like Black Friday. We systematically evaluate a broad spectrum of existing auto-bidding methods across these settings, encompassing classical control methods, RL-based methods, and recent generative methods. Besides these methods, we further propose a novel auto-bidding method based on flow-matching, termed BidFlow, which leverages the flow-matching method's expressive policy representation to effectively handle dynamic competitive environments. Online experiments on Kuaishou further show a +0.68% improvement in target cost, providing deployment evidence for the offline-online consistency of PlatformBid.

We consider $T$ repeated second-price auctions across $n$ pacing bidders with i.i.d. item arrivals, and show that it is computationally impossible for all bidders to achieve no-regret simultaneously while satisfying their respective budget or return-on-investment constraints. Therefore, in the prominent internet auction systems where buyers simultaneously deploy pacing algorithms or automated bidding agents, we cannot hope to achieve joint no-regret guarantees in general. We establish a deterministic relationship that high variance in online bidding systems implies high regret. By showing that one can extract a pacing equilibrium from a low-variance system, we prove PPAD-hardness of attaining joint no-regret. For several widely used bidding algorithms, we also show evidence from dynamical systems and numerical simulations that they can indeed display high-variance behavior through cycling, even on simple market instances.

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.