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. One can 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 nodes after their  long inactivity. However, due to a feedback mechanism the takeovers weaken the resilience of the attacking network. Then a conservation law that relates the feedback mechanism to the resilience dynamics for two competing networks can be defined. Within this formalism, the cost and optimal duration of an attack can be determined, allowing a network to evaluate the risk of initiating hostilities. Comment on how permanent attacks affect dynamical network robustness and use the network lifetime as a measure of dynamical network robustness will be given.

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