Stable Networks in Homogeneous Societies
Hellmann, Tim
Landwehr, Jakob
Network Formation
Pairwise Stability
Existence
Homogeneity
Convexity
Strategic Complements
Bonacich Centrality
ddc:330
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.
Center for Mathematical Economics, Bielefeld University
2014
info:eu-repo/semantics/workingPaper
doc-type:workingPaper
text
https://pub.uni-bielefeld.de/record/2708678
https://pub.uni-bielefeld.de/download/2708678/2902672
Hellmann T, Landwehr J. <em>Stable Networks in Homogeneous Societies</em>. Center for Mathematical Economics Working Papers. Vol 517. Bielefeld: Center for Mathematical Economics, Bielefeld University; 2014.
eng
info:eu-repo/semantics/altIdentifier/issn/0931-6558
info:eu-repo/semantics/openAccess