Decentralised Defence of a (Directed) Network Structure

We model the decentralised 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 an intelligent attacker who aims to maximise the flow-disruption by seeking to destroy one node. The set of the attacker’s potential targets is composed by critical nodes with highest brokerage power and therefore crucial to the system-flow. We show that a decentralised defence allocation is efficient when we assume perfect information: a centralised allocation of defence resources which minimises the flow-disruption coincides with a decentralised allocation. On the other hand, when we assume imperfect information, the decentralised allocation is inefficient.