Rankings in the Zerkani network by a game theoretical approach

TL;DR

This paper proposes new game-theoretic centrality measures, Banzhaf and Banzhaf-Owen values, to rank terrorists in a network by integrating topology and coalitional structures, with algorithms and real-world applications.

Contribution

Introduction of Banzhaf and Banzhaf-Owen centrality measures that incorporate network topology and coalitional structures, with algorithms and practical ranking applications.

Findings

Effective ranking of terrorists in the Zerkani network

Comparison shows differences between Banzhaf-based and Shapley/Owen rankings

Algorithms and R-code provided for practical implementation

Abstract

This paper introduces the Banzhaf and Banzhaf-Owen values as novel centrality measures for ranking terrorists in a network. This new approach let integrate the complete topology (i.e. nodes and edges) of the network and a coalitional structure on the nodes of the network. More precisely, the characteristics of the nodes (e.g., terrorists) of the network and their possible relationships (e.g., types of communication links), as well as coalitional information (e.g. level of hierarchies) independent of the network. First, for both centrality measures, we provide approximation algorithms and the corresponding R-codes. Second, as illustration, we rank the members of the Zerkani network, responsible for the attacks in Paris (2015) and Brussels (2016). Finally, we give a comparison between the rankings established by Banzhaf and Banzhaf-Owen and the rankings obtained when using the Shapley value (cf. Hamers et al., 2019) and the Owen value as centrality measures