Advertisement

Springer Nature is making SARS-CoV-2 and COVID-19 research free. View research | View latest news | Sign up for updates

On Robustness of Forward-looking in Sponsored Search Auction

  • 178 Accesses

  • 8 Citations

Abstract

We analyze the robustness of pure Nash Equilibria of sponsored search auctions, based on the forward-looking response function. To consider the robustness of such refined solution concept, we first study the convergence property of several adjustment schemes. Especially, we prove that under the randomized scheme, the auction always converges to a unique fixed point with probability one, whose revenue is equal to the celebrated VCG mechanism. Additionally, we study the robustness of such forward-looking strategic heuristic against aggressive selfish strategic heuristic called vindictive bidding. We investigate three types of such bidding strategies and substantiate that the pure Nash equilibrium still exists under two types even if there is an arbitrary portion of vindictive bidders.

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

References

  1. 1.

    Aggarwal, G., Goel, A., Motwani, R.: Truthful auctions for pricing search keywords. In: Proceedings of the 7th ACM Conference on Electronic Commerce (EC-06), pp. 1–7. Ann Arbor, USA, 11–15 June 2006

  2. 2.

    Brandt, F., Weiß, G.: Antisocial agents and vickrey auctions. In: Meyer, J.-J., Tambe, M. (eds.) Pre-proceedings of the 8th International Workshop on Agent Theories, Architectures, and Languages (ATAL-2001), pp. 120–132. Seattle, USA, 1–3 Aug. 2001

  3. 3.

    Bu, T.-M., Deng, X., Qi, Q.: Dynamics of strategic manipulation in ad-words auction. In: 3rd Workshop on Sponsored Search Auctions (SSA), in conjunction with WWW2007, Banff, Canada, 8 May 2007

  4. 4.

    Bu, T.-M., Deng, X., Qi, Q.: Forward looking Nash equilibrium for keyword auction. Inf. Process. Lett. 105(2), 41–46 (2008)

  5. 5.

    Cary, M., Das, A., Edelman, B., Giotis, I., Heimerl, K., Karlin, A.R., Mathieu, C., Schwarz, M.: Greedy bidding strategies for keyword auctions. In: Proceedings of the 8th ACM Conference on Electronic Commerce (EC-2007), pp. 262–271. San Diego, USA, 11–15 June 2007

  6. 6.

    Chen, X., Deng, X., Liu, B.J.: On incentive compatible competitive selection protocol. In: Proceedings of the 12th Annual International Computing and Combinatorics Conference (COCOON06), pp. 13–22. Taipei, Taiwan, 15–18 Aug. 2006

  7. 7.

    Clarke, E.H.: Multipart pricing of public goods. Public Choice 11(1), 11–33 (1971)

  8. 8.

    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)

  9. 9.

    Ganchev, K., Gabbard, R., Kulesza, A., Liu, Q., Tan, J., Kearns, M.: Empirical price modeling for sponsored search. In: Proceedings of the 3rd International Workshop on Internet and Network Economics, Wine2007. Springer, Berlin (2007)

  10. 10.

    Groves, T.: Incentives in teams. Econometrica 41(4), 617–631 (1973)

  11. 11.

    Kao, M.-Y., Li, X.-Y., Wang, W.: Output truthful versus input truthful: A new concept for algorithmic mechanism design. Unpublished (2006)

  12. 12.

    Kitts, B., Leblanc, B.: Optimal bidding on keyword auctions. Electronic Markets 14(3), 186–201 (2004). Special issue: Innovative Auction Markets

  13. 13.

    Lahaie, S.: An analysis of alternative slot auction designs for sponsored search. In: Proceedings of the 7th ACM Conference on Electronic Commerce (EC-06), pp. 218–227. Ann Arbor, USA, 11–15 June 2006

  14. 14.

    Liang, L., Qi, Q.: Cooperative or vindictive: Bidding strategies in sponsored search auction. In: Proceedings of the 3rd International Workshop on Internet and Network Economics (WINE2007), pp. 167–178. San Diego, USA, 12–14 Dec. 2007

  15. 15.

    Meek, C., Chickering, D.M., Wilson, D.B.: Stochastic and contingent-payment auctions. In: 1st Workshop on Sponsored Search Auctions (SSA), in conjunction with the ACM Conference on Electronic Commerce (EC-05). Vancouver, Canada, 5 June 2005

  16. 16.

    Myerson, R.: Incentive-compatibility and the bargaining problem. Econometrica 47, 61–73 (1979)

  17. 17.

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

  18. 18.

    Vickrey, W.: Counterspeculation, auctions, and competitive sealed tenders. J. Finance XVI(1), 8–37 (1961)

  19. 19.

    Vorobeychik, Y., Reeves, D.M.: Equilibrium analysis of dynamic bidding in sponsored search auctions. In: Proceedings of the 3rd International Workshop on Internet and Network Economics (WINE2007), pp. 155–166. San Diego, USA, 12–14 Dec. 2007

  20. 20.

    Zhou, Y., Lukose, R.: Vindictive bidding in keyword auctions. In: 2nd Workshop on Sponsored Search Auctions (SSA), in Conjunction with the ACM Conference on Electronic Commerce (EC-06). Ann Arbor, USA, 11 June 2006

Download references

Author information

Correspondence to Li Liang.

Additional information

Parts of this work were presented at the 3rd Workshop on Sponsored Search Auctions (SSA07) [3] and the 3rd International Workshop on Internet and Network Economics (WINE2007) [14].

The work described in this paper (or the equipment/facility) was supported by a grant from CityU (Project No. 7001989).

Research of T.-M. Bu is supported by grants of NSF of China (No. 60496321 and No. 90718013) and a grant of 863 program (No. 2007AA01Z189).

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Bu, T., Liang, L. & Qi, Q. On Robustness of Forward-looking in Sponsored Search Auction. Algorithmica 58, 970–989 (2010). https://doi.org/10.1007/s00453-009-9280-9

Download citation

Keywords

  • Sponsored search auction
  • Strategic manipulation
  • Forward-looking Nash equilibrium
  • Robustness