Hellmann, Tim
Tim
Hellmann
Landwehr, Jakob
Jakob
Landwehr
Stable Networks in Homogeneous Societies
Center for Mathematical Economics, Bielefeld University
2014
2014-12-10T13:50:39Z
2018-07-24T13:01:11Z
working_paper
https://pub.uni-bielefeld.de/record/2708678
https://pub.uni-bielefeld.de/record/2708678.json
0931-6558
urn:nbn:de:0070-pub-27086788
313396 bytes
application/x-download
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.