Abstract
This paper introduces a new centrality measure based on the Owen value to rank members in covert networks. In particular, we consider the Zerkani network responsible for the Paris attack of November 2015 and the Brussels attack of March 2016. We follow the line of research introduced in Hamers et al. [Handbook of the Shapley value. Taylor and Francis Group: CRC Press, pp 463–481 (2019)]. First, we consider two different appropriate cooperative games defined on the Zerkani network. Both games take into account the strengths of the links between its members and the individual contribution of its members. Second, for each game the Owen value is calculated, that provides a ranking of the members in the Zerkani network. For this calculation, we need to create a suitable partition of the members in the network, and, subsequently, we will use the approximation method introduced in Saavedra-Nieves et al. [The mathematics of the uncertain: A tribute to Pedro Gil. Springer, pp 347–356 (2018)]. Moreover, we can provide specific error bounds for the approximation of the Owen value. Finally, the obtained rankings are compared to the rankings established in Hamers et al. [Handbook of the Shapley value. Taylor and Francis Group: CRC Press, pp 463–481 (2019)].
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Notes
- 1.
This methodology ensures that each \(\pi \in \Pi _P(N)\) is equally likely. Alternatively, other sampling techniques, as stratified sampling, can be considered, that implies that not all permutations are taken with equal probability, see for instance Castro et al. (2017).
- 2.
Conditions to assure the equality between both games can be found in Algaba et al. (2001).
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Acknowledgements
The authors wish to thank Sascha Kurz for his invitation to contribute with a chapter to this volume devoted to Stefan Napel in recognition of his remarkable research career. They also thank two anonymous referees for their valuable comments and suggestions.
Financial support from R&D&I Project Grant PGC2018-097965-B-I00, funded by MCIN/ AEI/10.13039/501100011033/ and by “ERDF A way of making Europe”/EU is gratefully acknowledged. A. Saavedra-Nieves acknowledges the financial support of FEDER/Ministerio de Ciencia, Innovación y Universidades - Agencia Estatal de Investigación under grant MTM2017-87197-C3-3-P, and of the Xunta de Galicia through the European Regional Development Fund (Grupos de Referencia Competitiva ED431C 2021/24). Authors also thank the computational resources of the Centro de Supercomputación de Galicia (CESGA).
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Algaba, E., Prieto, A., Saavedra-Nieves, A., Hamers, H. (2023). Analyzing the Zerkani Network with the Owen Value. In: Kurz, S., Maaser, N., Mayer, A. (eds) Advances in Collective Decision Making. Studies in Choice and Welfare. Springer, Cham. https://doi.org/10.1007/978-3-031-21696-1_14
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