On the existence and uniqueness of pairwise stable networks

Tim Hellmann

International Journal of Game Theory, 2013, vol. 42, issue 1, 237 pages

Abstract: 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. Copyright Springer-Verlag 2013

Keywords: Network formation; Pairwise stability; Existence; Uniqueness; Convexity; Strategic complements; A14; C72; D85 (search for similar items in EconPapers)
Date: 2013
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Citations: View citations in EconPapers (38)

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DOI: 10.1007/s00182-012-0335-9

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