Verifying Nash Equilibria in PageRank Games on Undirected Web Graphs

Abstract

Abstract. 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 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.

Reputation games for undirected graphs

“…Note that the potential matrix Φ on G can be computed in O(n 2 ) time, by using Gaussian elimination methods for each column vector (Φ) v defined by equation (1). Since G is a tree we can apply elimination steps in post-order, where we consider v to be the root of G. There are at most n forward eliminations and backward substitutions because every node except v has only one parent.…”

“…This paper is an extended version of an earlier paper presented at ISAAC 2011 [1], which only covered the edge deletion model.…”

Preferential Attachment as a Unique Equilibrium

“…The one introduced by Fabrikant et al [8] (see also [19]) reaches an equilibrium on either the clique or the star graph, both of which rarely occur in large social networks. The PageRank game (see [2,6,9,13]) better fits the social network setting. In this game, the players represent web pages, and each player forms directed links to other players, with the goal of maximizing his PageRank.…”

Μελέτη Του Παγκόσμιου Ιστού Με Χρήση Θεωρίας Οικονομικών Και Παιγνίων

“…Για παράδειγμα σε ένα γράφημα που βρίσκεται σε ισορροπία, μία ιστοσελίδα θα διαθέτει εξερχόμενους υπερσυνδέσμους μόνο σε ιστοσελίδες που δείχνουν σε αυτήν. Στο ίδιο πλαίσιο κινείται και το μοντέλο των Avis et al [6,7] οι οποίοι μελετούν τα σημεία ισορροπίας παιγνίων σε μη κατευθυνόμενα γραφήματα που αναπαριστούν κοινωνικά δίκτυα, το οποίο ωστόσο δεν είναι κατάλληλο για την περίπτωσή μας.…”