Computing Optimal Bundles for Sponsored Search

  • Arpita Ghosh
  • Hamid Nazerzadeh
  • Mukund Sundararajan
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4858)

Abstract

context in sponsored search is additional information about a query, such as the user’s age, gender or location, that can change an advertisement’s relevance or an advertiser’s value for that query. Given a set of contexts, advertiser welfare is maximized if the search engine runs a separate auction for each context; however, due to lack of competition within contexts, this can lead to a significant loss in revenue. In general, neither separate auctions nor pure bundling need maximize revenue.

With this motivation, we study the algorithmic question of computing the revenue-maximizing partition of a set of items under a second-price mechanism and additive valuations for bundles. We show that the problem is strongly NP-hard, and present an algorithm that yields a \(\frac{1}{2}\)-approximation of the revenue from the optimal partition. The algorithm simultaneously yields a \(\frac{1}{2}\)-approximation of the optimal welfare, thus ensuring that the gain in revenue is not at the cost of welfare. Finally we show that our algorithm can be applied to the sponsored search setting with multiple slots, to obtain a constant factor approximation of the revenue from the optimal partition.

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References

  1. 1.
    Adams, W., Yellen, J.: Commodity bundling and the burden of monopoly. Quarterly Journal of Economics 90, 475–498 (1976)CrossRefGoogle Scholar
  2. 2.
    Aggarwal, G., Goel, A., Motwani, R.: Truthful auctions for pricing search keywords. In: EC 2006: Proceedings of the 7th ACM conference on Electronic commerce, pp. 1–7. ACM Press, New York (2006)CrossRefGoogle Scholar
  3. 3.
    Armstrong, M.: Multiproduct nonlinear pricing. Econometrica 6 64, 51–75 (1996)MATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    Armstrong, M.: Optimal multi-object auctions. Review of Economic Studies 67, 455–481 (2000)MATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    Bakos, Y., Brynjolfsson, E.: Bundling information goods: Pricing, profits, and efficiency. Management Science  (1999)Google Scholar
  6. 6.
    Brooks, N.: The Atlas Rank Report: How search engine rank impacts traffic. Atlas Institute  (July 2004)Google Scholar
  7. 7.
    Chakraborty, I.: Bundling decisions for selling multiple objects. Economic Theory 13, 723–733 (1999)MATHCrossRefGoogle Scholar
  8. 8.
    Edelman, B., Ostrovsky, M., Schwarz, M.: Internet advertising and the generalized second price auction: Selling billions of dollars worth of keywords. Stanford GSB Research Papers: Paper 1917 (2005)Google Scholar
  9. 9.
    Edelman, B., Schwarz, M.: Optimal auction design in a multi-unit environment: the case of sponsored search auctions. Manuscript in preparation  (2007)Google Scholar
  10. 10.
    Even-Dar, E., Kearns, M., Wortman, J.: Sponsored search with contexts. Third Workshop on Sponsored Search Auctions  (2007)Google Scholar
  11. 11.
    Jehiel, P., Meyer-ter-Vehn, M., Moldovanu, B.: Mixed bundling auctions. Journal of Economic Theory  (2007)Google Scholar
  12. 12.
    Likhodedov, A., Sandholm, T.: Approximating revenue-maximixing combinatorial auctions. In: Proceedings of the National Conference on Artificial Intelligence(AAAI) (2005)Google Scholar
  13. 13.
    Manelli, A., Vincent, D.: Bundling as an optimal selling mechanism for a multiple-good monopolist. Discussion paper, Arizona State University  (2001)Google Scholar
  14. 14.
    McAfee, P., McMillan, J., Whinston, M.: Multiproduct monopoly, commodity bundling, and correlation of values. The Quarterly Journal of Economics 104, 371–383 (1989)CrossRefMathSciNetGoogle Scholar
  15. 15.
    Palfrey, T.: Bundling decisions by a multiproduct monopolist with incomplete information. Econometrica 51, 463–484 (1983)MATHCrossRefGoogle Scholar
  16. 16.
    Varian, H.: Position auctions. To appear in International Journal of Industrial Organization  (2006)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • Arpita Ghosh
    • 1
  • Hamid Nazerzadeh
    • 2
  • Mukund Sundararajan
    • 2
  1. 1.Yahoo! Research 
  2. 2.Stanford University 

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