How do you defend a network?

Copyright © 2017 The Authors. 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 defense. 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 first provide a characterization of optimal attack and defense in terms of two classical concepts in graph theory: separators and transversals. This characterization permits a systematic study of the intensity of conflict (the resources spent on attack and defense) and helps us identify a new class of networks—windmill graphs—that minimize conflict. We then study security choices by individual nodes. Our analysis identifies the externalities and shows that the welfare costs of decentralized defense in networks can be very large.Both authors thank the European Research Area Complexity Net for financial support. Marcin Dziubi ́nskiwas supported by the Strategic Resilience of Networks project realized within the Homing Plus program ofthe Foundation for Polish Science and was co-financed by the European Union from the Regional Devel-opment Fund within Operational Programme Innovative Economy (grants for innovation). Sanjeev Goyalacknowledges financial support from a Keynes Fellowship and the Cambridge INET Institute