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On the existence and uniqueness of pairwise stable networks

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  • Tim Hellmann

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

Suggested Citation

  • Tim Hellmann, 2013. "On the existence and uniqueness of pairwise stable networks," International Journal of Game Theory, Springer;Game Theory Society, vol. 42(1), pages 211-237, February.
    • Handle: RePEc:spr:jogath:v:42:y:2013:i:1:p:211-237
    DOI: 10.1007/s00182-012-0335-9
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    References listed on IDEAS

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    More about this item

    Keywords

    Network formation; Pairwise stability; Existence; Uniqueness; Convexity; Strategic complements; A14; C72; D85;
    All these keywords.

    JEL classification:

    • A14 - General Economics and Teaching - - General Economics - - - Sociology of Economics
    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • D85 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Network Formation

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