Optimal Real-Time Bidding Strategy for Position Auctions in Online Advertising

Position auctions are widely studied in the context of sponsored search advertising, where multiple ad slots are sold in a single auction. In traditional sponsored search, bids are submitted at the keyword level, while recent works have explored transitioning to impression-level bidding using Real-Time Bidding (RTB) techniques to achieve finer bidding. However, position auctions introduce varying user appeal across different positions and more dynamic auction landscape, which RTB, originally devised for single-slot display advertising, fails to address adequately. In this work, we are the first to study the optimal bidding strategy for position auctions in RTB. The position auctions we study belong to a broader class, including both sponsored search and display advertising with multiple ad slots. In particular, we aim at maximizing the advertising value within the budget constraint for an advertiser. We mathematically formulate the problem with explicit modeling of position effects. By leveraging the Lagrange multiplier, we derive the optimal bid price and prove its uniqueness under mild assumptions. Efficient numeric methods are applied to obtain the solution practically. Extensive experiments are conducted on a public semi-synthetic dataset and a private industry dataset to validate the effectiveness and feasibility in practice.