Towards a Metric for Communication Network Vulnerability to Attacks: A Game Theoretic Approach

In this paper, we propose a quantification of the vulnerability of a communication network where links are subject to failures due to the actions of a strategic adversary. We model the adversarial nature of the problem as a 2-player game between a network manager who chooses a spanning tree of the network as communication infrastructure and an attacker who is trying to disrupt the communication by attacking a link. We use previously proposed models for the value of a network to derive payoffs of the players and propose the network’s expected loss-in-value as a metric for vulnerability. In the process, we generalize the notion of betweenness centrality: a metric largely used in Graph Theory to measure the relative importance of a link within a network. Furthermore, by computing and analyzing the Nash equilibria of the game, we determine the actions of both the attacker and the defender. The analysis reveals the existence of subsets of links that are more critical than the others. We characterize these critical subsets of links and related them to notions in Graph Theory. Using numerical examples, we show that critical subsets depend both on the value model and on the connectivity of the network. Finally we discuss how the critical subsets and the vulnerability metric can be used for network improvement.