Two-Stage Auctions with Bid Refinement for Online Advertising

To balance prediction accuracy and system latency, large-scale online ad auctions employ two-stage architectures. These systems first retrieve a candidate ads subset using coarse quality metrics before finalizing auction outcomes with refined metrics. However, existing implementations typically elicit user-specific bids only once, overlooking the impact of real-time quality metrics on advertiser valuations and thereby limiting allocation efficiency. Motivated by recent industry practice, we investigate the design of two-stage auctions that allow advertisers to submit and update their bids, with second-stage bids serving as refinements of the initial ones. We derive the incentive-compatible (IC) conditions and analyze the revenue properties of this two-stage auction. Notably, an additional entry fee is required to prevent inflated initial bids, which compromises the standard ex-post individual rationality (IR) property. To address this, we propose a dynamic two-stage auction that adopts realization-dependent entry fees with discounts. By leveraging historical bidding information, our mechanism guarantees approximate ex-ante IC across both stages and restores ex-post IR.