How do you defend a network?

Modern economies rely heavily on their infrastructure networks. These networks face threats ranging from natural disasters to human attacks. As networks are pervasive, the investments needed to protect them are very large; this motivates the study of targeted defence. What are the ‘key’ nodes to defend to maximize functionality of the network? What are the incentives of individual nodes to protect themselves in a networked environment and how do these incentives correspond to collective welfare? We provide a characterization of equilibrium attack and defence in terms of two classical concepts in graph theory – separators and transversals. We use this characterization to study the intensity of conflict (the resources spent on attack and defence) and the prospects of active conflict (when both adversary and defender target nodes for action) in networks. Finally, we show that welfare costs of decentralized defence can be very large