Influence of Network Mixing on Interdependent Security: Local Analysis

We study the impact of assortativity or network mixing on interdependent security. We employ a population game model to capture the interaction among many agents when agents are strategic and have various security measures they can choose to defend themselves. We model the interdependence in security among agents using a dependence network. The overall (local) network security seen by agents 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 network 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 depends on the cost effectiveness of security measures available to agents; if the security measures are not effective, increasing assortativity of the dependence network results in higher ARE. On the other hand, if the security measures are effective in fending off the damages and losses, increasing assortativity reduces the ARE experienced by agents.