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Prediction and Welfare in Ad Auctions

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Abstract

We study how standard auction objectives in sponsored search markets are affected by refinement in the prediction of ad relevance (click-through rates). As the prediction algorithm takes more features into account, its predictions become more refined; a natural question is whether this is desirable from the perspective of auction objectives. Our focus is on mechanisms that optimize for a convex combination of economic efficiency and revenue, and our starting point is the observation that the objective of such a mechanism can only improve with refined prediction, making refinement in the best interest of the search engine. We demonstrate that the impact of refinement on market efficiency is not always positive; nevertheless we are able to identify natural – and to some extent necessary – conditions under which refinement is guaranteed to also improve economic efficiency. Our main technical contribution is in explaining how refinement changes the ranking of advertisers by value (efficiency-optimal ranking), moving it either towards or away from their ranking by virtual value (revenue-optimal ranking). These results are closely related to the literature on signaling in auctions.

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Notes

  1. Clearly refinement should not be at the cost of using features that violate user privacy; in this work we leave aside issues of privacy to focus on welfare considerations of refinement.

  2. Throughout this paper, we use the term efficiency for economic rather than computational efficiency.

  3. The mechanisms used in practice, though not truthful, have equilibria that are allocation- and revenue-equivalent to the corresponding truthful mechanisms [6, 7]. Thus, we expect the gist our results to apply to practically used mechanisms in equilibrium. This raises an interesting open problem: As we show, refinement changes advertiser ranking in non-trivial ways; how do the equilibrium bids of the advertisers change in response? Will their level of granularity mirror that of the refinement? In other words, how does personalization affect the analysis of [6, 7]? The answer will depend on the informational assumptions of the model.

  4. The assumption that m ≥ n is without loss of generality. Advertisers/bidders are not to be confused with users, who are the ones submitting queries and not part of the auction.

  5. The assumption that p q, i ≠ 0 is without loss, to simplify the exposition.

  6. This definition matches that of Ghosh et al.’s deterministic clustering scheme [11]. In general a prediction scheme can be randomized, by including a distribution over relevance predictions for each part (cf. [8, 20]). Our results hold for randomized prediction schemes as well.

  7. The assumption of MHR values is common in the mechanism design literature (see, e.g., [17]). Many often-studied distributions are MHR, including the uniform, exponential and normal distributions, and those with log-concave densities [9].

  8. For our purpose we need not specify the pricing rule, because the second part of this lemma gives us a handle on revenue even without knowing the precise price form.

  9. In fact, it maximizes expected revenue among a larger class of mechanisms – Bayesian truthful and IR mechanisms.

  10. Mechanisms on the efficiency-revenue Pareto frontier are not to be confused with mechanisms that generate Pareto optimal outcomes, in which no bidder’s utility can be increased without decreasing another’s. Diakonikolas et al. study computational complexity aspects of the Pareto frontier; the difference between their work and ours is that we focus on trade-off optimal mechanisms, which are not required to realize every point on the Pareto optimal curve.

  11. A similar result holds for irregular position auctions, by replacing realized α-virtual values with their ironed counterparts.

  12. Note however that the result of Fu et al. [10] applies to completely general signals whereas we focus on the linear form standard in the context of sponsored search.

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Acknowledgments

The authors wish to thank Amir Najmi for suggesting the problem, Mohammad Mahdian for suggesting that Pareto optimal mechanisms are virtual value-based, and Qiqi Yan for many helpful comments. I. Talgam-Cohen gratefully acknowledges the support of the Hsieh Family Stanford Interdisciplinary Graduate Fellowship. For an early version see [24].

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Authors and Affiliations

  1. Google Inc., Mountain View, CA, 94043, USA

    Mukund Sundararajan

  2. Computer Science Department, Stanford University, Stanford, CA, 94305, USA

    Inbal Talgam-Cohen

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  1. Mukund Sundararajan
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  2. Inbal Talgam-Cohen
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Correspondence to Inbal Talgam-Cohen.

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Sundararajan, M., Talgam-Cohen, I. Prediction and Welfare in Ad Auctions. Theory Comput Syst 59, 664–682 (2016). https://doi.org/10.1007/s00224-016-9679-z

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