Network Disruption and the Common Enemy Effect

"The enemy of my enemy is my friend."

This common adage, which seems to be adhered to in social interactions (e.g. high school cliques or work relationships) as well as in political alliances within countries and between countries, describes the ability of groups or people to work together when they face an opponent, although otherwise they have little in common. In social psychology this phenomenon has been termed the "common enemy effect". Such group behavior can be studied using networks to depict the players within a group and the relationships between them. In this paper we study the effect of a common enemy on a model of network formation, where self-interested, myopic players can use links to build a network, knowing that they are facing a common enemy who can disrupt the links within the network and whose goal it is to minimize the overall value of the network. We find that introducing such a common enemy can lead to the formation of stable and efficient networks which would not be stable without the threat of disruption. However, we also find that fragmented networks as well as the empty networks are also stable. While the common enemy can thus have a positive effect on the incentives of players to form an efficient network, it can also lead to fragmentation and disintegration of the network.