Pricing Ad Slots with Consecutive Multi-unit Demand

  • Xiaotie Deng
  • Paul Goldberg
  • Yang Sun
  • Bo Tang
  • Jinshan Zhang
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8146)


We consider the optimal pricing problem for a model of the rich media advertisement market, as well as other related applications. In this market, there are multiple buyers (advertisers), and items (slots) that are arranged in a line such as a banner on a website. Each buyer desires a particular number of consecutive slots and has a per-unit-quality value v i (dependent on the ad only) while each slot j has a quality q j (dependent on the position only such as click-through rate in position auctions). Hence, the valuation of the buyer i for item j is v i q j . We want to decide the allocations and the prices in order to maximize the total revenue of the market maker.

A key difference from the traditional position auction is the advertiser’s requirement of a fixed number of consecutive slots. Consecutive slots may be needed for a large size rich media ad. We study three major pricing mechanisms, the Bayesian pricing model, the maximum revenue market equilibrium model and an envy-free solution model. Under the Bayesian model, we design a polynomial time computable truthful mechanism which is optimum in revenue. For the market equilibrium paradigm, we find a polynomial time algorithm to obtain the maximum revenue market equilibrium solution. In envy-free settings, an optimal solution is presented when the buyers have the same demand for the number of consecutive slots. We conduct a simulation that compares the revenues from the above schemes and gives convincing results.


mechanism design revenue advertisement auction 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Alaei, S.: Bayesian combinatorial auctions: Expanding single buyer mechanisms to many buyers. In: Proceedings of the 52nd IEEE Symposium on Foundations of Computer Science (FOCS), pp. 512–521 (2011)Google Scholar
  2. 2.
    Ausubel, L., Cramton, P.: Demand revelation and inefficiency in multi-unit auctions. In: Mimeograph, University of Maryland (1996)Google Scholar
  3. 3.
    Bhattacharya, S., Goel, G., Gollapudi, S., Munagala, K.: Budget constrained auctions with heterogeneous items. In: Proceedings of the 42nd ACM Symposium on Theory of Computing, STOC 2010, New York, NY, USA, pp. 379–388 (2010)Google Scholar
  4. 4.
    Cai, Y., Daskalakis, C., Matthew Weinberg, S.: An algorithmic characterization of multi-dimensional mechanisms. In: Proceedings of the 43rd Annual ACM Symposium on Theory of Computing (2012)Google Scholar
  5. 5.
    Cai, Y., Daskalakis, C., Matthew Weinberg, S.: Optimal multi-dimensional mechanism design: Reducing revenue to welfare maximization. In: Proceedings of the 2012 IEEE 53rd Annual Symposium on Foundations of Computer Science, FOCS 2012 (2012)Google Scholar
  6. 6.
    Cantillon, E., Pesendorfer, M.: Combination bidding in multi-unit auctions. C.E.P.R. Discussion Papers (February 2007)Google Scholar
  7. 7.
    Chen, N., Deng, X., Goldberg, P.W., Zhang, J.: On revenue maximization with sharp multi-unit demands. CoRR abs/1210.0203 (2012)Google Scholar
  8. 8.
    Demange, G., Gale, D., Sotomayor, M.: Multi-item auctions. The Journal of Political Economy, 863–872 (1986)Google Scholar
  9. 9.
    Edelman, B., Ostrovsky, M., Schwarz, M.: Internet advertising and the generalized second-price auction: Selling billions of dollars worth of keywords. American Economic Review 97(1), 242–259 (2007)CrossRefGoogle Scholar
  10. 10.
    Engelbrecht-Wiggans, R., Kahn, C.M.: Multi-unit auctions with uniform prices. Economic Theory 12(2), 227–258 (1998)MathSciNetCrossRefMATHGoogle Scholar
  11. 11.
    Gul, F., Stacchetti, E.: Walrasian equilibrium with gross substitutes. Journal of Economic Theory 87(1), 95–124 (1999)MathSciNetCrossRefMATHGoogle Scholar
  12. 12.
    Lahaie, S.: An analysis of alternative slot auction designs for sponsored search. In: Proceedings of the 7th ACM Conference on Electronic Commerce, EC 2006, New York, NY, USA, pp. 218–227 (2006)Google Scholar
  13. 13.
    Myerson, R.B.: Optimal auction design. Mathematics of Operations Research 6(1), 58–73 (1981)MathSciNetCrossRefMATHGoogle Scholar
  14. 14.
    Rothkopf, M.H., Pekeč, A., Harstad, R.M.: Computationally manageable combinational auctions. Management Science 44(8), 1131–1147 (1998)CrossRefMATHGoogle Scholar
  15. 15.
    Shapley, L.S., Shubik, M.: The Assignment Game I: The Core. International Journal of Game Theory 1(1), 111–130 (1971)MathSciNetCrossRefMATHGoogle Scholar
  16. 16.
    Varian, H.R.: Position auctions. International Journal of Industrial Organization 25(6), 1163–1178 (2007)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Xiaotie Deng
    • 1
    • 2
  • Paul Goldberg
    • 3
  • Yang Sun
    • 4
  • Bo Tang
    • 2
  • Jinshan Zhang
    • 2
  1. 1.Department of Computer ScienceShanghai Jiaotong UniversityChina
  2. 2.Department of Computer ScienceUniversity of LiverpoolUK
  3. 3.Department of Computer ScienceOxford UniversityUK
  4. 4.Department of Computer ScienceCity University of Hong KongHong Kong

Personalised recommendations