Optimal Real-time Bidding Policies for Contract Fulfillment in Second Price Auctions

We study a real-time bidding problem resulting from a set of contractual obligations stipulating that a firm win a specified number of heterogenous impressions or ad placements over a defined duration in a realtime auction. The contracts specify item targeting criteria (which may be overlapping), and a supply requirement. Using the Pontryagin maximum principle, we show that the resulting continuous time and time inhomogenous planning problem can be reduced into a finite dimensional convex optimization problem and solved to optimality. In addition, we provide algorithms to update the bidding plan over time via a receding horizon. Finally, we provide numerical results based on real data and show a connection to production-transportation problems. keywords Computational Advertising; Realtime Bidding; Optimal Control; Auction Theory; Second Price Auction; Production Transportation Problem Acknowledgement We acknowledge the support of the Natural Sciences and Engineering Research Council of Canada (NSERC), [funding reference number 518418-2018]. Cette recherche a été financée par le Conseil de recherches en sciences naturelles et en génie du Canada (CRSNG), [numéro de référence 518418-2018]. Relevant code to be made available at github.com/RJTK 1 ar X iv :2 01 2. 10 00 1v 1 [ ee ss .S Y ] 1 8 D ec 2 02 0

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