Pairwise stable networks in homogeneous societies

We study general properties of pairwise stable networks in homogeneous societies, i.e. when agents' utilities differ only with respect to their network position while their names do not matter. Rather than assuming a particular functional form of utility, we impose general link externality conditions on utility such as ordinal convexity and ordinal strategic complements. Depending on these rather weak notions of link externalities, we show that pairwise stable networks of various structure exist. For stronger versions of the convexity and strategic complements conditions, we are even able to characterize all pairwise stable networks: they are nested split graphs (NSG). We illustrate these results with many examples from the literature, including utility funtions that arise from games with strategic complements played on the network and utility funtions that depend on centrality measures such as Bonacich centrality.