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On the existence and uniqueness of pairwise stable networks

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  • Tim Hellmann

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    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

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    Bibliographic Info

    Article provided by Springer in its journal International Journal of Game Theory.

    Volume (Year): 42 (2013)
    Issue (Month): 1 (February)
    Pages: 211-237

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    Handle: RePEc:spr:jogath:v:42:y:2013:i:1:p:211-237

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    Related research

    Keywords: Network formation; Pairwise stability; Existence; Uniqueness; Convexity; Strategic complements; A14; C72; D85;

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    1. Bloch, Francis & Jackson, Matthew O., 2007. "The formation of networks with transfers among players," Journal of Economic Theory, Elsevier, vol. 133(1), pages 83-110, March.
    2. Francis Bloch & Matthew Jackson, 2006. "Definitions of equilibrium in network formation games," International Journal of Game Theory, Springer, vol. 34(3), pages 305-318, October.
    3. Venkatesh Bala & Sanjeev Goyal, 2000. "A Noncooperative Model of Network Formation," Econometrica, Econometric Society, vol. 68(5), pages 1181-1230, September.
    4. Dutta, Bhaskar & Mutuswami, Suresh, 1996. "Stable Networks," Working Papers 971, California Institute of Technology, Division of the Humanities and Social Sciences.
    5. Pascal Billand & Christophe Bravard & Sudipta Sarangi, 2011. "Local Spillovers, Convexity and the Strategic Substitutes Property in Networks," Post-Print halshs-00574265, HAL.
    6. Berno Buechel & Tim Hellmann, 2012. "Under-connected and over-connected networks: the role of externalities in strategic network formation," Review of Economic Design, Springer, vol. 16(1), pages 71-87, March.
    7. Goyal, Sanjeev & Vega-Redondo, Fernando, 2007. "Structural holes in social networks," Journal of Economic Theory, Elsevier, vol. 137(1), pages 460-492, November.
    8. Subhadip Chakrabarti & Robert Gilles, 2007. "Network potentials," Review of Economic Design, Springer, vol. 11(1), pages 13-52, June.
    9. Antoni Calvó-Armengol & Rahmi İlkılıç, 2009. "Pairwise-stability and Nash equilibria in network formation," International Journal of Game Theory, Springer, vol. 38(1), pages 51-79, March.
    10. Goyal, S. & Joshi, S., 1999. "Bilateralism and free trade," Econometric Institute Research Papers EI 9953-/A, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    11. Monderer, Dov & Shapley, Lloyd S., 1996. "Potential Games," Games and Economic Behavior, Elsevier, vol. 14(1), pages 124-143, May.
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    Cited by:
    1. Tim Hellmann & Mathias Staudigl, 2012. "Evolution of Social networks," Working Papers 470, Bielefeld University, Center for Mathematical Economics.

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