The cost of attack in competing networks

TL;DR

This paper models the dynamics and costs of attacks between competing networks, revealing how attack strategies impact resilience and identifying optimal attack durations through a formal conservation law.

Contribution

It introduces a novel model of network competition that accounts for feedback effects and resilience trade-offs, providing a framework to evaluate attack costs and risks.

Findings

Longer attacks increase damage but weaken attacker resilience.

Optimal attack duration balances damage inflicted and self-preservation.

A conservation law links feedback mechanisms to resilience dynamics.

Abstract

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 nodes after their long inactivity. However, due 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.