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 the 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 a subset of the set of middleman nodes and producers. These are the critical nodes with highest brokerage power in a directed network 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 and involves no reallocation of defence resources between the nodes. Finally, for a given connected graph, by increasing the link-density we can reduce the set of middleman nodes and thus the number of the potential targets. This also decreases the probability of a successful attack.