Theoretical Economics 12 (2017), 331–376
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How do you defend a network?
Marcin Konrad Dziubiński, Sanjeev Goyal
Abstract
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
Keywords: Infrastructure, costs of conflict, windmill graph, attack, defence
JEL classification: D1, D8, C7
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