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Online Allocation and Display Ads Optimization with Surplus Supply

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Web and Internet Economics (WINE 2022)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 13778))

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Abstract

In this work, we study a scenario where a publisher seeks to maximize its total revenue across two sales channels: guaranteed contracts that promise to deliver a certain number of impressions to the advertisers, and spot demands through an Ad Exchange. On the one hand, if a guaranteed contract is not fully delivered, it incurs a penalty for the publisher. On the other hand, the publisher might be able to sell an impression at a high price in the Ad Exchange. How does a publisher maximize its total revenue as a sum of the revenue from the Ad Exchange and the loss from the under-delivery penalty? We study this problem parameterized by supply factor f: a notion we introduce that, intuitively, captures the number of times a publisher can satisfy all its guaranteed contracts given its inventory supply. In this work we present a fast simple deterministic algorithm with the optimal competitive ratio. The algorithm and the optimal competitive ratio are a function of the supply factor, penalty, and the distribution of the bids in the Ad Exchange.

Beyond the yield optimization problem, classic online allocation problems such as online bipartite matching of Karp-Vazirani-Vazirani [25] and its vertex-weighted variant of Aggarwal et al. [2] can be studied in the presence of the additional supply guaranteed by the supply factor. We show that a supply factor of f improves the approximation factors from \(1-1/e\) to \(f-fe^{-1/f}\). Our approximation factor is tight and approaches 1 as \(f \rightarrow \infty \).

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Notes

  1. 1.

    We use the terms demand and capacity interchangeably. Technically, offline nodes do not have any capacities, they just have demands. However, for a node that demands \(n_a\) impressions, assigning more than \(n_a\) impressions is always suboptimal, so essentially \(n_a\) can be interpreted as a capacity as well. The AdEx offline node is an exception where the capacity is infinite, in the sense that it is always profitable to assign an additional online node to AdEx.

  2. 2.

    We later discuss relaxing the penalty c to depend on the advertiser a.

  3. 3.

    Unweighted edges for contractual advertisers is fine because these contracts are mostly based on the number of impressions delivered. In a few cases the contracts are based on the number of clicks or conversions, in which case the edges will be weighted based on the probability of click or conversion. Contracts based on impressions form such a large majority, that having unweighted edges, is almost wlog.

  4. 4.

    Note that \(A_j\) is a random set depending on the realization of AdEx rewards over all queries.

  5. 5.

    The assumption on a fixed support, can be relaxed using a standard discretization approach at a small cost in the competitive ratio that depends on this discretization.

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Authors and Affiliations

  1. Google, New York, NY, USA

    Melika Abolhassani, Hossein Esfandiari, Balasubramanian Sivan, Yifeng Teng & Creighton Thomas

  2. University of Salzberg, Salzburg, Austria

    Yasamin Nazari

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  1. Melika Abolhassani
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  2. Hossein Esfandiari
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Correspondence to Yifeng Teng .

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  1. Aarhus University, Aarhus, Denmark

    Kristoffer Arnsfelt Hansen

  2. Tsinghua University, Beijing, China

    Tracy Xiao Liu

  3. Rotman School of Management, University of Toronto, Toronto, ON, Canada

    Azarakhsh Malekian

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Abolhassani, M., Esfandiari, H., Nazari, Y., Sivan, B., Teng, Y., Thomas, C. (2022). Online Allocation and Display Ads Optimization with Surplus Supply. In: Hansen, K.A., Liu, T.X., Malekian, A. (eds) Web and Internet Economics. WINE 2022. Lecture Notes in Computer Science, vol 13778. Springer, Cham. https://doi.org/10.1007/978-3-031-22832-2_3

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  • DOI: https://doi.org/10.1007/978-3-031-22832-2_3

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