Skip to main content

On the α-Sensitivity of Nash Equilibria in PageRank-Based Network Reputation Games

  • Conference paper

Part of the Lecture Notes in Computer Science book series (LNTCS,volume 5598)

Abstract

Web search engines use link-based reputation systems (e.g. PageRank) to measure the importance of web pages, giving rise to the strategic manipulations of hyperlinks by spammers and others to boost their web pages’ reputation scores. Hopcroft and Sheldon [10] study this phenomenon by proposing a network formation game in which nodes strategically select their outgoing links in order to maximize their PageRank scores. They pose an open question in [10] asking whether all Nash equilibria in the PageRank game are insensitive to the restart probability α of the PageRank algorithm. They show that a positive answer to the question would imply that all Nash equilibria in the PageRank game must satisfy some strong algebraic symmetry, a property rarely satisfied by real web graphs. In this paper, we give a negative answer to this open question. We present a family of graphs that are Nash equilibria in the PageRank game only for certain choices of α.

Keywords

  • Random Walk
  • Nash Equilibrium
  • Reputation System
  • Outgoing Link
  • Reputation Score

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

This is a preview of subscription content, access via your institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   39.99
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   54.99
Price excludes VAT (Canada)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Bartlett, M.S.: An Inverse Matrix Adjustment Arising in Discriminant Analysis. Annals of Mathematical Statistics 22(1), 107–111 (1951) MR40068

    CrossRef  MathSciNet  MATH  Google Scholar 

  2. Bianchini, M., Gori, M., Scarselli, F.: Inside PageRank. ACM Trans. Inter. Tech. 5(1), 92–128 (2005)

    CrossRef  Google Scholar 

  3. Brin, S., Pagep, L.: The anatomy of a large-scale hypertextual Web search engine. Computer Networks and ISDN Systems 30(1–7), 107–117 (1998)

    CrossRef  Google Scholar 

  4. Cheng, A., Friedman, E.: Manipulability of PageRank under sybil strategies. In: Proceedings of the First Workshop of Networked Systems (NetEcon 2006) (2006)

    Google Scholar 

  5. Friedman, E., Resnick, P., Sami, R.: Manipulation-resistant reputation systems. In: Nisan, N., Roughgarden, T., Tardos, E., Vazirani, V. (eds.) Algorithmic Game Theory. Cambridge University Press, Cambridge (2007)

    Google Scholar 

  6. Gyöngyi, Z., Garcia-Molina, H.: Web spam taxonomy. In: First International Workshop on Adversarial Information Retrieval on the Web (2005)

    Google Scholar 

  7. Gyöngyi, Z., Garcia-Molina, H.: Link spam alliances. In: Proceedings of the 31st International Conference on Very Large Databases, pp. 517–528. ACM, New York (2005)

    Google Scholar 

  8. Hogg, T., Adamic, L.: Enhancing reputation mechanisms via online social networks. In: Proceedings of the 5th ACM Conference on Electronic Commerce, pp. 236–237 (2004)

    Google Scholar 

  9. Hopcroft, J., Sheldon, D.: Manipulation-Resistant Reputations Using Hitting Time. In: Bonato, A., Chung, F.R.K. (eds.) WAW 2007. LNCS, vol. 4863, p. 68. Springer, Heidelberg (2007)

    CrossRef  Google Scholar 

  10. Hopcroft, J., Sheldon, D.: Network Reputation Games, Manuscript, eCommons@Cornell (October 2008), http://ecommons.library.cornell.edu/handle/1813/11579

  11. Kamvar, S.D., Schlosser, M.T., Garcia-Molina, H.: The eigentrust algorithm for reputation management in P2P networks. In: WWW 2003: Proceedings of the 12th international World Wide Web Conference, pp. 640–651. ACM Press, New York (2003)

    Google Scholar 

  12. Tardos, É., Wexler, T.: Network formation games and the potential function method. In: Nisan, N., Roughgarden, T., Tardos, E., Vazirani, V. (eds.) Algorithmic Game Theory. Cambridge University Press, Cambridge (2007)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and Permissions

Copyright information

© 2009 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Chen, W., Teng, SH., Wang, Y., Zhou, Y. (2009). On the α-Sensitivity of Nash Equilibria in PageRank-Based Network Reputation Games. In: Deng, X., Hopcroft, J.E., Xue, J. (eds) Frontiers in Algorithmics. FAW 2009. Lecture Notes in Computer Science, vol 5598. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-02270-8_9

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-02270-8_9

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-02269-2

  • Online ISBN: 978-3-642-02270-8

  • eBook Packages: Computer ScienceComputer Science (R0)