Decentralized Defence of a (Directed) Network Structure

We model the decentralized defence choice of agents connected in a directed graph and exposed to an external threat. The network allows players to receive goods from one or more producers through directed paths. Each agent is endowed with a finite and divisible defence resource that can be allocated to their own security or to that of their peers. The external threat is represented by either a random attack on one of the nodes or by an intelligent attacker who aims to maximize the flow-disruption by seeking to destroy one node. We show that under certain conditions a decentralized defence allocation is efficient when we assume the attacker to be strategic: a centralized allocation of defence resources which minimizes the flow-disruption coincides with a decentralized equilibrium allocation. On the other hand, when we assume a random attack, the decentralized allocation is likely to diverge from the central planner’s allocation.