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Stable Networks in Homogeneous Societies

Tim Hellmann and Jakob Landwehr
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Tim Hellmann: Center for Mathematical Economics, Bielefeld University
Jakob Landwehr: Center for Mathematical Economics, Bielefeld University

No 517, Center for Mathematical Economics Working Papers from 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.

Keywords: Network Formation; Pairwise Stability; Existence; Homogeneity; Convexity; Strategic Complements; Bonacich Centrality (search for similar items in EconPapers)
New Economics Papers: this item is included in nep-gth, nep-mic, nep-net, nep-soc and nep-upt
Date: 2014-12-10
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https://pub.uni-bielefeld.de/download/2708678/2902672 First Version, 2014 (application/x-download)

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Persistent link: https://EconPapers.repec.org/RePEc:bie:wpaper:517

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