The anatomy of a large-scale hypertextual Web search engine
WWW7 Proceedings of the seventh international conference on World Wide Web 7
The Eigentrust algorithm for reputation management in P2P networks
WWW '03 Proceedings of the 12th international conference on World Wide Web
Enhancing reputation mechanisms via online social networks
EC '04 Proceedings of the 5th ACM conference on Electronic commerce
ACM Transactions on Internet Technology (TOIT)
VLDB '05 Proceedings of the 31st international conference on Very large data bases
Manipulation-resistant reputations using hitting time
WAW'07 Proceedings of the 5th international conference on Algorithms and models for the web-graph
Verifying nash equilibria in pagerank games on undirected web graphs
ISAAC'11 Proceedings of the 22nd international conference on Algorithms and Computation
Reputation games for undirected graphs
Discrete Applied Mathematics
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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 .