Verifying Nash Equilibria in PageRank Games on Undirected Web Graphs

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 PageRank 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) time algorithm for a tree, and a parametric O(2n) time algorithm for general graphs, where k is the maximum vertex degree in any biconnected component of the graph.