# Stable Networks in Homogeneous Societies

Hellmann T, Landwehr J (2014) Center for Mathematical Economics Working Papers; 517.

Bielefeld: Center for Mathematical Economics, Bielefeld University.

Download

IMW_working_paper_517.pdf
313.40 KB

*Working Paper*|

*English*

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

Publishing Year

ISSN

PUB-ID

### Cite this

Hellmann T, Landwehr J.

*Stable Networks in Homogeneous Societies*. Center for Mathematical Economics Working Papers. Vol 517. Bielefeld: Center for Mathematical Economics, Bielefeld University; 2014.Hellmann, T., & Landwehr, J. (2014).

*Stable Networks in Homogeneous Societies*(Center for Mathematical Economics Working Papers, 517). Bielefeld: Center for Mathematical Economics, Bielefeld University.Hellmann, T., and Landwehr, J. (2014). Stable Networks in Homogeneous Societies.

*Center for Mathematical Economics Working Papers*, 517, Bielefeld: Center for Mathematical Economics, Bielefeld University.Hellmann, T., & Landwehr, J., 2014.

*Stable Networks in Homogeneous Societies*, Center for Mathematical Economics Working Papers, no.517, Bielefeld: Center for Mathematical Economics, Bielefeld University. T. Hellmann and J. Landwehr,

*Stable Networks in Homogeneous Societies*, Center for Mathematical Economics Working Papers, vol. 517, Bielefeld: Center for Mathematical Economics, Bielefeld University, 2014. Hellmann, T., Landwehr, J.: Stable Networks in Homogeneous Societies. Center for Mathematical Economics Working Papers, 517. Center for Mathematical Economics, Bielefeld University, Bielefeld (2014).

Hellmann, Tim, and Landwehr, Jakob.

*Stable Networks in Homogeneous Societies*. Bielefeld: Center for Mathematical Economics, Bielefeld University, 2014. Center for Mathematical Economics Working Papers. 517.**All files available under the following license(s):**

**Copyright Statement:**

**This Item is protected by copyright and/or related rights.**[...]

**Main File(s)**

File Name

IMW_working_paper_517.pdf
313.40 KB

Access Level

Open Access

Last Uploaded

2016-04-14T14:02:06Z

This data publication is cited in the following publications:

This publication cites the following data publications:

**Material in PUB:**

**Later Version**

Pairwise stable networks in homogeneous societies

Hellmann T, Landwehr J (2018) Center for Mathematical Economics Working Papers; 517, Version Januar 2018.

Bielefeld: Center for Mathematical Economics.

Hellmann T, Landwehr J (2018) Center for Mathematical Economics Working Papers; 517, Version Januar 2018.

Bielefeld: Center for Mathematical Economics.