Analyzing the Zerkani Network with the Owen Value

  1. Algaba, Encarnación 1
  2. Prieto, Andrea 2
  3. Saavedra-Nieves, Alejandro 4
  4. Hamers, Herbert 3
  1. 1 Matemática Aplicada II and Instituto de Matemáticas de la Universidad de Sevilla, Sevilla, Spain
  2. 2 Matemática Aplicada II, Escuela Superior de Ingenieros, Camino de los Descubrimientos, Sevilla, Spain
  3. 3 CentER, Department of Econometrics and Operations Research and TIAS Business School, Tilburg University, Tilburg, The Netherlands
  4. 4 Departamento de Estatística, Análise Matemática e Optimización, Universidade de Santiago de Compostela, Santiago de Compostela, Spain
Mostrar afiliaciones +
Libro:
Studies in Choice and Welfare

ISSN: 1614-0311,  2197-8530

ISBN: 9783031216954,  9783031216961

Año de publicación: 2023

Páginas: 225-242

Tipo: Capítulo de Libro

DOI: 10.1007/978-3-031-21696-1_14 GOOGLE SCHOLAR lock_openAcceso abierto editor

Resumen

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)].

Referencias bibliográficas

  • Algaba, E., Fragnelli, V., & Sánchez-Soriano, J. (Eds.). (2019). Handbook of the Shapley value. Taylor and Francis Group: CRC Press.
  • Algaba, E., Prieto, A., & Saavedra-Nieves, A. (2022). Rankings in the Zerkani network by a game theoretical approach. Working paper 1-28,
  • Algaba, E., Bilbao, J. M., Borm, P., & López, J. J. (2000). The position value for union stable systems. Mathematical Methods of Operations Research, 52, 221–236.
  • Algaba, E., Bilbao, J. M., & López, J. J. (2001). A unified approach to restricted games. Theory and Decision, 50, 333–345.
  • Algaba, E., Bilbao, J. M., Fernández García, J. R., & López, J. J. (2003). Computing power indices in weighted multiple majority games. Mathematical Social Sciences, 46(1), 63–80.
  • Algaba, E., Bilbao, J. M., & Fernández, J. R. (2007). The distribution of power in the European Constitution. European Journal of Operational Research, 176(3), 1752–1766.
  • Alonso-Meijide, J. M., & Bowles, C. (2005). Generating functions for coalitional power indices: An application to the IMF. Annals of Operations Research, 137(1), 21–44.
  • Banzhaf, J. F. (1965). Weighted voting doesn’t work: A mathematical analysis. Rutgers Law Review, 19, 317–343.
  • Basra, R., & Neumann, P. (2016). Criminal pasts, terrorist futures: European jihadists and the new crime-terror nexus. Perspectives on Terrorism, 10(6), 25–40.
  • Castro, J., Gómez, D., & Tejada, J. (2009). Polynomial calculation of the Shapley value based on sampling. Computers & Operations Research, 36, 1726–1730.
  • Castro, J., Gómez, D., Molina, E., & Tejada, J. (2017). Improving polynomial estimation of the Shapley value by stratified random sampling with optimum allocation. Computers & Operations Research, 82, 180–188.
  • Costa, J. (2016). A polynomial expression for the Owen value in the maintenance cost game. Optimization, 65(4), 797–809.
  • Deng, X., & Papadimitriou, C. H. (1994). On the complexity of cooperative solution concepts. Mathematics of Operations Research, 19(2), 257–266.
  • Farley, J. D. (2003). Breaking AlQaeda cells: A mathematical analysis of counterterrorism operations. Studies in conflict and terrorism, 26(6), 299–314.
  • Fragnelli, V., García-Jurado, I., Norde, H., Patrone, F., & Tijs, S. (2000). How to share railways infrastructure costs? In Game practice: Contributions from applied game theory (pp. 91–101). Springer.
  • Gartenstein-Ross, D., & Barr, N. (2016, April 27). Recent attacks illuminates the Islamic State’s Europe attack network. The Jamestown Foundation. https://jamestown.org/program/hot-issue-recent-attacks-illuminate-the-islamic-states-europe-attack-network/
  • Hamers, H., Husslage, B., & Lindelauf, R. (2019). Analysing ISIS Zerkani network using the Shapley value. In E. Algaba, V. Fragnelli, & J. Sánchez-Soriano (Eds.), Handbook of the Shapley value (pp. 463–481). CRC Press, Taylor and Francis Group.
  • Husslage, B., Borm, P., Burg, T., Hamers, H., & Lindelauf, R. (2015). Ranking terrorists in networks: A sensitivity analysis of Al Qaeda’s 9/11 attack. Social Networks, 42, 1–7.
  • Klerks, P. (2001). The network paradigm applied to criminal organizations. Connections, 24, 53–65.
  • Koschade, S. (2006). A social network analysis of Jemaah Islamiyah: The applications to counterterrorism and intelligence. Studies in Conflict and Terrorism, 29(6), 559–575.
  • Krebs, V. E. (2002). Mapping networks of terrorist cells. Connections, 24, 43–52.
  • Kurz, S., & Napel, S. (2014). Heuristic and exact solutions to the inverse power index problem for small voting bodies. Annals of Operations Research, 42, 137–163.
  • Lindelauf, R., Hamers, H., & Husslage, B. (2013). Cooperative game theoretic centrality analysis of terrorist networks: The cases of Jemaah Islamiyah and Al Qaeda. European Journal of Operational Research, 229, 230–238.
  • Littlechild, S. C., & Owen, G. (1973). A simple expression for the Shapley value in a special case. Management Science, 20(3), 370–372.
  • Myerson, R. (1977). Graphs and cooperation in games. Mathematics of Operations Research, 2, 225–229.
  • Owen, G. (1977). Values of games with a priori unions. In R. Henn & O. Moeschlin (Eds.), Mathematical economics and game theory (pp. 76–88). Springer.
  • Owen, G. (1982). Modification of the Banzhaf-Coleman index for games with a priori unions. In M. J. Holler (Ed.), Power, voting, and voting power (pp. 232–238). Springer.
  • Saavedra-Nieves, A., García-Jurado, I., & Fiestras-Janeiro, M. G. (2018). Estimation of the Owen value based on sampling. In E. Gil, E. Gil, J. G. Gil, & M. Á. Gil (Eds.), The mathematics of the uncertain: A tribute to Pedro Gil (pp. 347–356). Springer.
  • Shapley, L. S. (1953). A value for n-person games. Contributions to the Theory of Games, 2(28), 307–317.
  • Sparrow, M. (1991). The application of network analysis to criminal intelligence: An assessment of the prospects. Social Networks, 13(3), 251–274.
  • van Campen, T., Hamers, H., Husslage, B., & Lindelauf, R. (2018). A new approximation method for the Shapley value applied to the WTC 9/11 terrorist attack. Social Networks Analysis and Mining, 8(1), 1–12.
  • van den Nouweland, A., Borm, P., & Tijs, S. H. (1992). Allocation rules for hypergraph communication situations. International Journal of Game Theory, 20, 255–268.
  • Vázquez-Brage, M., van den Nouweland, A., & García-Jurado, I. (1997). Owen’s coalitional value and aircraft landing fees. Mathematical Social Sciences, 34(3), 273–286.
  • Wise, W. M. (2005). Indonesia’s war on terror. United States-Indonesia Society.