View in EDS

Pairwise stable networks in homogeneous societies with weak link externalities.

Saved in:
Bibliographic Details
Title: Pairwise stable networks in homogeneous societies with weak link externalities.
Authors: Hellmann, Tim1 (AUTHOR) t.hellmann@soton.ac.uk
Source: European Journal of Operational Research. Jun2021, Vol. 291 Issue 3, p1164-1179. 16p.
Subjects: Externalities, Strategy games, Centrality
Abstract: • Existence of pairwise Nash stable networks of particular structure is established. • All pairwise stable networks are characterized by particular classes of networks. • Results do not require functional form of utility only anonymity condition is used. • Weak link externality conditions (strategic complements, convexity) are exploited. • Application to many examples in the literature of network formation is shown. 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. [ABSTRACT FROM AUTHOR]
Copyright of European Journal of Operational Research is the property of Elsevier B.V. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
Database: Engineering Source
Description
Abstract:• Existence of pairwise Nash stable networks of particular structure is established. • All pairwise stable networks are characterized by particular classes of networks. • Results do not require functional form of utility only anonymity condition is used. • Weak link externality conditions (strategic complements, convexity) are exploited. • Application to many examples in the literature of network formation is shown. 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. [ABSTRACT FROM AUTHOR]
ISSN:03772217
DOI:10.1016/j.ejor.2020.09.025