Pairwise stable networks in homogeneous societies with weak link externalities

Abstract

We study general properties of pairwise stable and pairwise Nash stable networks when players are ex-ante homogeneous. 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 Nash 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. We illustrate these results with many examples from the literature, including utility functions that arise from games with strategic complements played on the network and utility functions that depend on centrality measures such as Bonacich centrality.