Verifying Nash Equilibria in PageRank Games on Undirected Web Graphs [chapter]

David Avis, Kazuo Iwama, Daichi Paku
2011 Lecture Notes in Computer Science  
J. Hopcroft and D. Sheldon originally introduced the PageRank game to investigate the self-interested behavior of web authors who want to boost their PageRank by using game theoretical approaches. The PageRank game is a multiplayer game where players are the nodes in a directed web graph and they place their outlinks to maximize their PageRank value. They give best response strategies for each player and characterize properties of α-insensitive Nash equilibria. In this paper we consider
more » ... games for undirected web graphs, where players are free to delete any of their bidirectional links if they wish. We study the problem of determining whether the given graph represents a Nash equilibrium or not. We give an O(n 2 ) time algorithm for a tree, and a parametric O(2 k n 4 ) time algorithm for general graphs, where k is the maximum vertex degree in any biconnected component of the graph.
doi:10.1007/978-3-642-25591-5_43 fatcat:4vzpzg3mlzfyfhausnikz24zvu