Pairwise stable networks in homogeneous societies with weak link externalities

We study general properties of pairwise stable and Nash networks when players are ex-ante homogeneous. Rather than assuming a particular functional form utility, we impose link externality conditions on utility such as ordinal convexity strategic complements. Depending these rather weak notions externalities, show that various structure exist. For stronger versions the complements conditions, even able to characterize all networks: they nested split graphs. illustrate results with many examples from literature, including functions arise games played network depend centrality measures Bonacich centrality.