Role of network topology in cybersecurity

We study how an underlying network property affects network security when nodes are rational and have four choices - i) invest in protection, ii) purchase (incomplete coverage) insurance, iii) invest in protection and purchase insurance, or iv) do nothing. More specifically, using a population game model, we examine how the degree distribution of nodes influences their choices at Nash equilibria (NEs) and overall security level. We first show that there exists a degree threshold at NEs so that only the populations with degrees greater than or equal to the threshold invest in protection. Second, as the weighted degree distribution of nodes becomes stochastically larger, the risk or threat posed by a neighbor decreases, even though the aforementioned degree threshold tends to rise, hence only nodes with increasingly higher degrees invest in protection, at the same time. Third, we show that the social optimum also possesses similar properties. Finally, we derive an upper bound on the price of anarchy, which is an affine function of the average degree of nodes. This upper bound is tight in that it is achieved in some scenarios.