Sponsored Search Auctions with Markovian Users

  • Gagan Aggarwal
  • Jon Feldman
  • S. Muthukrishnan
  • Martin Pál
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5385)


Sponsored search involves running an auction among advertisers who bid in order to have their ad shown next to search results for specific keywords. The most popular auction for sponsored search is the “Generalized Second Price” (GSP) auction where advertisers are assigned to slots in the decreasing order of their score, which is defined as the product of their bid and click-through rate. One of the main advantages of this simple ranking is that bidding strategy is intuitive: to move up to a more prominent slot on the results page, bid more. This makes it simple for advertisers to strategize. However this ranking only maximizes efficiency under the assumption that the probability of a user clicking on an ad is independent of the other ads shown on the page. We study a Markovian user model that does not make this assumption. Under this model, the most efficient assignment is no longer a simple ranking function as in GSP. We show that the optimal assignment can be found efficiently (even in near-linear time). As a result of the more sophisticated structure of the optimal assignment, bidding dynamics become more complex: indeed it is no longer clear that bidding more moves one higher on the page. Our main technical result is that despite the added complexity of the bidding dynamics, the optimal assignment has the property that ad position is still monotone in bid. Thus even in this richer user model, our mechanism retains the core bidding dynamics of the GSP auction that make it useful for advertisers.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Aggarwal, G., Feldman, J., Muthukrishnan, S., Pál, M.: Sponsored search auctions with Markovian users (May 2008), http://arxiv.org/abs/0805.0766
  2. 2.
    Aggarwal, G., Feldman, J., Muthukrishnan, S., Pál, M.: Sponsored search auctions with Markovian users. In: Workshop on Ad Auctions (July 2008)Google Scholar
  3. 3.
    Aggarwal, G., Goel, A., Motwani, R.: Truthful auctions for pricing search keywords. In: ACM Conference on Electronic Commerce (EC) (2006)Google Scholar
  4. 4.
    Archer, A., Tardos, E.: Truthful mechanisms for one-parameter agents. In: Proc. of the 42nd IEEE Symposium on Foundations of Computer Science (2001)Google Scholar
  5. 5.
    Athey, S., Ellison, G.: Position auctions with consumer search. Levine’s Bibliography 122247000000001633, UCLA Department of Economics (October 2007)Google Scholar
  6. 6.
    Clarke, E.: Multipart pricing of public goods. Public Choice 11, 17–33 (1971)CrossRefGoogle Scholar
  7. 7.
    Craswell, N., Zoeter, O., Taylor, M., Ramsey, B.: An experimental comparison of click position-bias models. In: WSDM 2008 (2008)Google Scholar
  8. 8.
    Edelman, B., Ostrovsky, M., Schwarz, M.: Internet advertising and the generalized second price auction: Selling billions of dollars worth of keywords. In: Second workshop on sponsored search auctions (2006)Google Scholar
  9. 9.
    Feldman, J., Muthukrishnan, S.: Algorithmic Methods for Sponsored Search Advertising, pp. 91–124. Springer, Heidelberg (2008)Google Scholar
  10. 10.
    Goel, G., Mehta, A.: Online budgeted matching in random input models with applications to adwords. In: SODA (2008)Google Scholar
  11. 11.
    Groves, T.: Incentives in teams. Econometrica 41(4), 617–631 (1973) MathSciNetCrossRefMATHGoogle Scholar
  12. 12.
    Gunawardana, A., Meek, C.: Aggregators and contextual effects in search ad markets. In: Workshop on Targeting and Ranking for Online Advertising (2008)Google Scholar
  13. 13.
    Kempe, D., Mahdian, M.: Cascade model for externalities in sponsored search. In: Workshop on Internet Ad Auctions (2008)Google Scholar
  14. 14.
    Krishnamurthy, R., Boral, H., Zaniolo, C.: Optimization of nonrecursive queries. In: VLDB 1986, pp. 128–137 (1986)Google Scholar
  15. 15.
    Lahie, S., Pennock, D., Saberi, A., Vohra, R.: Sponsored Search Auctions. In: Algorithmic Game Theory, pp. 699–716. Cambridge University Press, Cambridge (2007)CrossRefGoogle Scholar
  16. 16.
    Szymanski, B.K., Lee, J.-S.: Impact of ROI on bidding and revenue in sponsored search advertisement auctions. In: 2nd Wkshp Sponsored Search Auctions (2006)Google Scholar
  17. 17.
    Varian, H.: Position auctions. International Journal of Industrial Organization 25(6), 1163–1178 (2007)CrossRefGoogle Scholar
  18. 18.
    Vickrey, W.: Counterspeculation, auctions and competitive-sealed tenders. Finance 16(1), 8–37 (1961)MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Gagan Aggarwal
    • 1
  • Jon Feldman
    • 1
  • S. Muthukrishnan
    • 1
  • Martin Pál
    • 1
  1. 1.Google, Inc., 76 Ninth Avenue, 4th Floor, New York, NY, 10011, 1600 Amphitheatre Pkwy, Mountain View, CA, 94043USA

Personalised recommendations