Effects of Degree Correlations in Interdependent Security: Good or Bad?

We study the influence of degree correlations or network mixing on interdependent security. We model the interdependence in security among agents using a dependence graph and employ a population game model to capture the interaction among many agents when they are strategic and have various security measures they can choose to defend themselves. The overall network security is measured by what we call the average risk exposure (ARE) from neighbors, which is proportional to the total (expected) number of attacks in the network. We first show that there exists a unique pure-strategy Nash equilibrium of a population game. Then, we prove that as the agents with larger degrees in the dependence graph see higher risks than those with smaller degrees, the overall network security deteriorates in that the ARE experienced by agents increases and there are more attacks in the network. Finally, using this finding, we demonstrate that the effects of network mixing on ARE depend on the (cost) effectiveness of security measures available to agents; if the security measures are not effective, increasing assortativity of dependence graph results in higher ARE. On the other hand, if the security measures are effective at fending off the damages and losses from attacks, increasing assortativity reduces the ARE experienced by agents.