Weighted network decapitation: the economics of iterated attack and defense

Vulnerability of networks (e.g. peer-to-peer networks, social networks, etc.) against one-shot decapitation attacks has been addressed several times in the literature. A first study on how a network can best defend itself by replenishing nodes and rewiring edges after decapitation was made by Nagaraja and Anderson. We extend the work of those authors by: i) considering weighted networks; ii) taking into account the economic aspects of the attack and defense strategies, namely the cost of node destruction/replenishment and subtler costs such as the average path length increase or the privacy degradation.