Skip to main content
Log in

Prediction and Welfare in Ad Auctions

  • Published:
Theory of Computing Systems Aims and scope Submit manuscript


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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Subscribe and save

Springer+ Basic
EUR 32.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or Ebook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1
Fig. 2

Similar content being viewed by others


  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 mn 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.


  1. Aggarwal, G., Goel, A., Motwani, R.: Truthful auctions for pricing search keywords. In: Proceedings of 7th ACM Conference on Economics and Computation (EC), pp. 1–7 (2006)

  2. Aggarwal, G., Goel, G., Mehta, A.: Efficiency of (revenue-)optimal mechanisms. In: The 10th ACM Conference on Electronic Commerce, pp. 235–242 (2009)

  3. Clarke, E.H.: Multipart pricing of public goods. Public Choice 11, 17–33 (1971)

    Article  Google Scholar 

  4. Daskalakis, C., Pierrakos, G.: Simple, optimal and efficient auctions. In: Proceedings of 7th Conference on Web and Internet Economics (WINE) (2011)

  5. Diakonikolas, I., Papadimitriou, C., Pierrakos, G., Singer, Y.: Efficiency-revenue trade-offs in auctions. In: Proceedings of ICALP (2012)

  6. Edelman, B., Ostrovsky, M., Schwarz, M.: Internet advertising and the generalized second-price auction: Selling billions of dollars worth of keywords. Am. Econ. Rev. 97(1), 242–259 (2007)

    Article  Google Scholar 

  7. Edelman, B., Schwarz, M.: Optimal auction design and equilibrium selection in sponsored search auctions. Am. Econ. Rev. 100(2), 597–602 (2010)

    Article  Google Scholar 

  8. Emek, Y., Feldman, M., Gamzu, I., Paes Leme, R., Tennenholtz, M.: Signaling schemes for revenue maximization. ACM Trans. Econ. Comput. 2(2), 5 (2014)

  9. Ewerhart, C.: Optimal design and ρ-concavity, working paper (2009)

  10. Fu, H., Jordan, P., Mahdian, M., Nadav, U., Talgam-Cohen, I., Vassilvitskii, S.: Ad auctions with data. In: Proceedings of 5th International Symposium on Algorithmic Game Theory (SAGT), pp. 168–179 (2012)

  11. Ghosh, A., Nazerzadeh, H., Sundararajan, M.: Computing optimal bundles for sponsored search. In: Proceedings of 3rd Conference on Web and Internet Economics (WINE), pp. 576–583 (2007)

  12. Graepel, T., Candela, J.Q., Borchert, T., Herbrich, R.: Web-scale Bayesian click-through rate prediction for sponsored search advertising in Microsoft’s Bing search engine. In: 27th International Conference on Machine Learning (ICML), pp. 13–20 (2010)

  13. Groves, T.: Incentives in teams. Econometrica 41, 617–631 (1973)

    Article  MathSciNet  MATH  Google Scholar 

  14. Lahaie, S., Pennock, D.M.: Revenue analysis of a family of ranking rules for keyword auctions. In: Proceedings of 8th ACM Conference on Economics and Computation (EC), pp. 50–56 (2007)

  15. Lahaie, S., Pennock, D.M., Saberi, A., Vohra, R.V.: Sponsored search auctions. In: Nisan, N., Roughgarden, T., Tardos, É., Vazirani, V. (eds.) Algorithmic Game Theory, chap. 28, pp. 699–716. Cambridge University Press (2007)

  16. Likhodedov, A., Sandholm, T.: Auction mechanism for optimally trading off revenue and efficiency. In: Proceedings of 4th ACM Conference on Economics and Computation (EC), pp. 212–213 (2003)

  17. McAfee, R., McMillan, J.: Auctions and bidding. J. Econ. Lit. 25(2), 699–738 (1987)

    MATH  Google Scholar 

  18. Mehta, A., Saberi, A., Vazirani, U., Vazirani, V.: Adwords and generalized on-line matching. J. ACM 54(5), 22 (2007)

  19. Milgrom, P., Weber, R.J.: A theory of auctions and competitive bidding. Econometrica 50, 1089–1122 (1982)

    Article  MATH  Google Scholar 

  20. Miltersen, P.B., Sheffet, O.: Send mixed signals: Earn more, work less. In: Proceedings of 13th ACM Conference on Economics and Computation (EC), pp. 234–247 (2012)

  21. Myerson, R.: Optimal auction design. Math. Oper. Res. 6(1), 58–73 (1981)

    Article  MathSciNet  MATH  Google Scholar 

  22. Myerson, R., Satterthwaite, M.: Efficient mechanisms for bilaterial trade. J. Econ. Theory 29(1), 265–281 (1983)

    Article  MathSciNet  MATH  Google Scholar 

  23. Neeman, Z.: The effectiveness of English auctions. Games Econ. Behav. 43(2), 214–238 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  24. Sundararajan, M., Talgam-Cohen, I.: Prediction and welfare in ad auctions. In: Proceedings of 7th International Symposium on Algorithmic Game Theory (SAGT), pp 267–278 (2014)

  25. Taleghan, M.A., Hamdaoui, B.: Efficiency-revenue optimality tradeoffs in dynamic spectrum allocation. In: IEEE Global Telecommunications Conference (GLOBECOM) (2010)

  26. Varian, H.R.: Position auctions. Int. J. Ind. Organ. 25(6), 1163–1178 (2007)

    Article  Google Scholar 

  27. Vickrey, W.: Counterspeculation, auctions, and competitive sealed tenders. J. Financ. 16, 8–37 (1961)

    Article  MathSciNet  Google Scholar 

Download references


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].

Author information

Authors and Affiliations


Corresponding author

Correspondence to Inbal Talgam-Cohen.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Sundararajan, M., Talgam-Cohen, I. Prediction and Welfare in Ad Auctions. Theory Comput Syst 59, 664–682 (2016).

Download citation

  • Published:

  • Issue Date:

  • DOI: