The cost of attack in competing networks.
Real-world attacks can be interpreted as the result of competitive interactions between networks, ranging from predator-prey networks to networks of countries under economic sanctions. Although the purpose of an attack is to damage a target network, it also curtails the ability of the attacker, which must choose the duration and magnitude of an attack to avoid negative impacts on its own functioning. Nevertheless, despite the large number of studies on interconnected networks, the consequences of initiating an attack have never been studied. Here, we address this issue by introducing a model of network competition where a resilient network is willing to partially weaken its own resilience in order to more severely damage a less resilient competitor. The attacking network can take over the competitor's nodes after their long inactivity. However, owing to a feedback mechanism the takeovers weaken the resilience of the attacking network. We define a conservation law that relates the feedback mechanism to the resilience dynamics for two competing networks. Within this formalism, we determine the cost and optimal duration of an attack, allowing a network to evaluate the risk of initiating hostilities.
Center for Polymer Studies and Department of Physics, Boston University, Boston, MA 02215, USA Faculty of Civil Engineering, University of Rijeka, 51000 Rijeka, Croatia Zagreb School of Economics and Management, 10000 Zagreb, Croatia.
B
B
Podobnik
Faculty of Natural Sciences, University of Zagreb, 10000 Zagreb, Croatia davorh@phy.hr.
D
http://orcid.org/0000-0002-0411-8474
D
Horvatic
Center for Polymer Studies and Department of Physics, Boston University, Boston, MA 02215, USA Rudjer Boskovic Institute, Centre for Informatics and Computing, 10000 Zagreb, Croatia.
T
http://orcid.org/0000-0002-8037-8198
T
Lipic
Faculty of Natural Sciences and Mathematics, University of Maribor, Koroška cesta 160, 2000 Maribor, Slovenia Department of Physics, Faculty of Sciences, King Abdulaziz University, Jeddah, Saudi Arabia.
M
http://orcid.org/0000-0002-3087-541X
M
Perc
Center for Biomedical Technology (UPM), 28223 Pozuelo de Alarcón, Madrid, Spain Complex Systems Group, Rey Juan Carlos University, 28933 Móstoles, Madrid, Spain.
J M
http://orcid.org/0000-0002-9345-599X
JM
Buldú
Center for Polymer Studies and Department of Physics, Boston University, Boston, MA 02215, USA.
H E
http://orcid.org/0000-0003-2800-4495
HE
Stanley
D006801:Humans; D018803:Models, Economic; D014857:Warfare
attacks; complex networks; interactive networks; network vulnerability; robustness; socioeconomic systems