Network disruption and the common-enemy effect

We study the effect of a common enemy on the connections-model of network formation, where self-interested players can use links to build a network, knowing that they face a common enemy who can disrupt the links or nodes of the network. The goal of the common enemy is to minimize the sum of the benefits players obtain from the network. We find that for large linking costs, introducing such a common enemy can lead to the formation of pairwise stable and efficient networks which would not be pairwise stable without the threat of disruption. The reason is the large reduction in payoffs caused by disruption as soon as one player fails to maintain a link. However, we also find that for small linking costs, the empty network is pairwise stable under disruption, whereas it is not in the absence of disruption. The reason is that in the presence of disruption a link that is unilaterally formed is automatically targeted (or one of the players forming the link is automatically targeted). While the common enemy can thus have a positive effect on the incentives of the players to form an efficient network, it can also lead to the disintegration of the network.