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Stable Networks in Homogeneous Societies

Author

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  • Hellmann, Tim

    (Center for Mathematical Economics, Bielefeld University)

  • Landwehr, Jakob

    (Center for Mathematical Economics, Bielefeld University)

Abstract

We study the structure of pairwise stable networks from a very general point. Rather than assuming a particular functional form of utility, we simply assume that the society is homogeneous, i.e. that agents' utilities differ only with respect to their network position while their names do not matter. Existence of certain stable network structures is then implied by fairly general assumptions on externalities between links. Depending on the form of link externalities, either the empty or complete network are always pairwise stable, stable symmetric networks exist, or stable networks with a connected subgroup exist. If the society becomes more homogeneous, then it is possible to characterize the set of all pairwise stable networks: they are nested split graphs (NSG). We illustrate these results with many examples from the literature, including utility profiles that depend on centrality measures such as Bonacich centrality. In particular, for low discount factors every pairwise stable network is an NSG if utility is given by Bonacich centrality.

Suggested Citation

  • Hellmann, Tim & Landwehr, Jakob, 2014. "Stable Networks in Homogeneous Societies," Center for Mathematical Economics Working Papers 517, Center for Mathematical Economics, Bielefeld University.
  • Handle: RePEc:bie:wpaper:517
    as

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    File URL: https://pub.uni-bielefeld.de/download/2708678/2902672
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    References listed on IDEAS

    as
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    Cited by:

    1. Philippe Bich & Lisa Morhaim, 2020. "On the Existence of Pairwise Stable Weighted Networks," Mathematics of Operations Research, INFORMS, vol. 45(4), pages 1393-1404, November.
    2. Gauer, Florian & Hellmann, Tim, 2017. "Strategic formation of homogeneous bargaining networks," Center for Mathematical Economics Working Papers 529, Center for Mathematical Economics, Bielefeld University.
    3. Gauer, Florian, 2015. "Strategic Formation of Homogeneous Bargaining Networks," VfS Annual Conference 2015 (Muenster): Economic Development - Theory and Policy 112943, Verein für Socialpolitik / German Economic Association.
    4. Gauer, F. & Hellmann, T., 2017. "Strategic formation of homogeneous bargaining networks," Games and Economic Behavior, Elsevier, vol. 106(C), pages 51-74.

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    Keywords

    Network Formation; Pairwise Stability; Existence; Homogeneity; Convexity; Strategic Complements; Bonacich Centrality;
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