The common enemy effect under strategic network formation and disruption

Social psychology studies the “common enemy effect”, the phenomenon that members of a group work together when they face an opponent, although they otherwise have little in common. An interesting scenario is the formation of an information network where group members individually sponsor costly links. Suppose that ceteris paribus, an outsider appears who aims to disrupt the information flow within the network by deleting some of the links. The question is how the group responds to this common enemy. We address this question for the homogeneous connections model of strategic network formation, with two-way flow of information and without information decay. For sufficiently low linkage costs, the external threat can lead to a more connected network, a positive common enemy effect. For very high but not prohibitively high linkage costs, the equilibrium network can be minimally connected and efficient in the absence of the external threat whereas it is always empty and inefficient in the presence of the external threat, a negative common enemy effect. For intermediate linkage costs, both connected networks and the empty network are Nash for certain cost ranges.