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Frequency capping in online advertising

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Abstract

We study the following online problem. There are n advertisers. Each advertiser \(a_i\) has a total demand \(d_i\) and a value \(v_i\) for each supply unit. Supply units arrive one by one in an online fashion, and must be allocated to an agent immediately. Each unit is associated with a user, and each advertiser \(a_i\) is willing to accept no more than \(f_i\) units associated with any single user (the value \(f_i\) is called the frequency cap of advertiser \(a_i\)). The goal is to design an online allocation algorithm maximizing the total value. We first show a deterministic \(3/4\)-competitiveness upper bound, which holds even when all frequency caps are \(1\), and all advertisers share identical values and demands. A competitive ratio approaching \(1-1/e\) can be achieved via a reduction to a different model considered by Goel and Mehta (WINE ‘07: Workshop on Internet and Network, Economics: 335–340, 2007). Our main contribution is analyzing two \(3/4\)-competitive greedy algorithms for the cases of equal values, and arbitrary valuations with equal integral demand to frequency cap ratios. Finally, we give a primal-dual algorithm which may serve as a good starting point for improving upon the ratio of \(1-1/e\).

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Notes

  1. In contrast, sponsored search advertisers typically pay-per-click or per action, and usually have budgets, rather than a demand, or quota, on the total number of impressions.

  2. See, e.g., http://www.marketingterms.com/dictionary/frequency_cap.

  3. While it might be argued that displaying an ad more than once to a user reinforces the advertiser’s message, repeated display without an upper limit clearly diminishes value.

  4. While \(1-1/e\) is the best possible competitive factor for the model of Goel and Mehta (2007) since this model captures the adwords model of Mehta et al. (2007), the frequency capping problem does not generalize the adwords model of Mehta et al. (2007). Therefore, it does not follow that \(1-1/e\) is an upper bound for our problem.

  5. Following Lemma 5, every advertiser with an exhausted demand can be “blamed” for at most \(y_i\) impressions in B. The definition of \(h\) attempts to isolate the advertiser \(a_h\) which is to be blamed for the fact that \(x \in B\).

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Acknowledgments

We are extremely grateful to Ning Chen for several helpful discussions, and for first suggesting the total demand algorithm. Research supported in part by ISF Grant 954/11, and by BSF Grant 2010426. Research supported in part by the Google Inter-University Center for Electronic Markets, by ISF Grant 954/11, and by BSF Grant 2010426.

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Authors and Affiliations

  1. Department of Statistics and Operations Research, Tel Aviv University, Tel Aviv, Israel

    Niv Buchbinder

  2. Institute of Core Computing Science, EPFL, Lausanne, Switzerland

    Moran Feldman

  3. Information Science Department, Cornell University, Ithaca, NY, USA

    Arpita Ghosh

  4. Computer Science Department, Technion, Haifa, Israel

    Joseph Naor

Authors
  1. Niv Buchbinder
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  2. Moran Feldman
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  3. Arpita Ghosh
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  4. Joseph Naor
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Corresponding author

Correspondence to Moran Feldman.

Additional information

A preliminary version of this paper appeared in the Proceedings of the Algorithms and Data Structures Symposium (WADS), New York, NY, 2011.

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Buchbinder, N., Feldman, M., Ghosh, A. et al. Frequency capping in online advertising. J Sched 17, 385–398 (2014). https://doi.org/10.1007/s10951-014-0367-z

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