Game-theoretic Network Centrality: A Review

Abstract

Game-theoretic centrality is a flexible and sophisticated approach to identify the most important nodes in a network. It builds upon the methods from cooperative game theory and network theory. The key idea is to treat nodes as players in a cooperative game, where the value of each coalition is determined by certain graph-theoretic properties. Using solution concepts from cooperative game theory, it is then possible to measure how responsible each node is for the worth of the network.The literature on the topic is already quite large, and is scattered among game-theoretic and computer science venues. We review the main gametheoretic network centrality measures from both bodies of literature and organize them into two categories: those that are more focused on the connectivity of nodes, and those that are more focused on the synergies achieved by nodes in groups. We present and explain each centrality, with a focus on algorithms and complexity.

Game Theoretic Foundations of the Gately Power Measure for Directed Networks

“…We refer to Tarkowski et al [4] for an overview of the literature on cooperative game theoretic constructions of centrality measures in directed networks. This authority can also be psychological and can be an influence on reputational features in the relationship.…”

“…Here, the set of dominated nodes is treated as a collective resource that is distributed according to a chosen principle. In the Gately measure, this is the proportional distribution 4 . This stands in contrast to the individualistic perspective of the β-measure.…”

Generalised Gately Values of Cooperative Games

“…The concept of network centrality has emerged from sociology and social network analysis (Barabási, 2016) into the field of game theory, giving rise to game theoretic methods to measure the most important and dominant nodes in a social network (Gómez et al, 2003;Pozo et al, 2011;Bloch et al, 2016;Tarkowski et al, 2018). A well-accepted approach is to formulate a cooperative game that captures features of a social network and then apply a cooperative solution concept to this associated game.…”

“…For a recent overview of these game-theoretic approaches we also refer toGómez et al (2003),Pozo et al (2011) andTarkowski et al (2018).…”