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.

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Abstract
We study general properties of pairwise stable networks in homogeneous societies, i.e. when agents' utilities differ only with respect to their network position while their names do not matter. Rather than assuming a particular functional form of utility, we impose general link externality conditions on utility such as ordinal convexity and ordinal strategic complements. Depending on these rather weak notions of link externalities, we show that pairwise stable networks of various structure exist. For stronger versions of the convexity and strategic complements conditions, we are even able to characterize all pairwise stable networks: they are nested split graphs (NSG). We illustrate these results with many examples from the literature, including utility funtions that arise from games with strategic complements played on the network and utility funtions that depend on centrality measures such as Bonacich centrality.
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Hellmann T, Landwehr J. Pairwise stable networks in homogeneous societies. Center for Mathematical Economics Working Papers. Vol 517 Version Januar 2018. Bielefeld: Center for Mathematical Economics; 2018.
Hellmann, T., & Landwehr, J. (2018). Pairwise stable networks in homogeneous societies (Center for Mathematical Economics Working Papers, 517) Version Januar 2018. Bielefeld: Center for Mathematical Economics.
Hellmann, T., and Landwehr, J. (2018). Pairwise stable networks in homogeneous societies. Center for Mathematical Economics Working Papers, 517, Version Januar 2018. Bielefeld: Center for Mathematical Economics.
Hellmann, T., & Landwehr, J., 2018. Pairwise stable networks in homogeneous societies, Center for Mathematical Economics Working Papers, no.517, Version Januar 2018., Bielefeld: Center for Mathematical Economics.
T. Hellmann and J. Landwehr, Pairwise stable networks in homogeneous societies, Center for Mathematical Economics Working Papers, vol. 517, Version Januar 2018., Bielefeld: Center for Mathematical Economics, 2018.
Hellmann, T., Landwehr, J.: Pairwise stable networks in homogeneous societies. Center for Mathematical Economics Working Papers, 517, Version Januar 2018. Center for Mathematical Economics, Bielefeld (2018).
Hellmann, Tim, and Landwehr, Jakob. Pairwise stable networks in homogeneous societies. Version Januar 2018. Bielefeld: Center for Mathematical Economics, 2018. Center for Mathematical Economics Working Papers. 517.
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Earlier Version
Stable Networks in Homogeneous Societies
Hellmann T, Landwehr J (2014) Center for Mathematical Economics Working Papers; 517.
Bielefeld: Center for Mathematical Economics, Bielefeld University.

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