Pairwise stable networks in homogeneous societies with weak link externalities
Pairwise stable networks in homogeneous societies with weak link externalities
We study general properties of pairwise stable and pairwise Nash stable networks when players are ex-ante homogeneous. 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 Nash 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. We illustrate these results with many examples from the literature, including utility functions that arise from games with strategic complements played on the network and utility functions that depend on centrality measures such as Bonacich centrality.
Convexity, Network formation, Noncooperative games, Strategic complements
Hellmann, Tim
e03b4edd-3010-4f6d-831e-86e4b3d6cbe0
Hellmann, Tim
e03b4edd-3010-4f6d-831e-86e4b3d6cbe0
Hellmann, Tim
(2020)
Pairwise stable networks in homogeneous societies with weak link externalities.
European Journal of Operational Research.
(doi:10.1016/j.ejor.2020.09.025).
Abstract
We study general properties of pairwise stable and pairwise Nash stable networks when players are ex-ante homogeneous. 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 Nash 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. We illustrate these results with many examples from the literature, including utility functions that arise from games with strategic complements played on the network and utility functions that depend on centrality measures such as Bonacich centrality.
Text
HomogeneousSocietiesEJOR_r2
- Accepted Manuscript
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Accepted/In Press date: 20 September 2020
e-pub ahead of print date: 28 September 2020
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Publisher Copyright:
© 2020 Elsevier B.V.
Keywords:
Convexity, Network formation, Noncooperative games, Strategic complements
Identifiers
Local EPrints ID: 444174
URI: http://eprints.soton.ac.uk/id/eprint/444174
ISSN: 0377-2217
PURE UUID: ec4fb019-94e6-4df4-8e90-e8e254eee37c
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Date deposited: 30 Sep 2020 16:30
Last modified: 17 Mar 2024 05:56
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