On the existence and uniqueness of pairwise stable networks

In this paper we show how externalities between links affect the existence and uniqueness of pairwise stable (PS) networks. For this we introduce the properties ordinal convexity (concavity) and ordinal strategic complements (substitutes) of utility functions on networks. It is shown that there exists at least one PS network if the profile of utility functions is ordinal convex and satisfies the ordinal strategic complements property. On the other hand, ordinal concavity and ordinal strategic substitutes are sufficient for some uniqueness properties of PS networks. Additionally, we elaborate on the relation of the link externality properties to definitions in the literature.