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

  • Wei Chen
  • Shang-Hua Teng
  • Yajun Wang
  • Yuan Zhou
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5598)


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.


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.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Wei Chen
    • 1
  • Shang-Hua Teng
    • 1
  • Yajun Wang
    • 1
  • Yuan Zhou
    • 2
  1. 1.Microsoft ResearchUSA
  2. 2.Tsinghua UniversityChina

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