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Pairwise stable networks in homogeneous societies with weak link externalities

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  • Hellmann, Tim

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.

Suggested Citation

  • Hellmann, Tim, 2021. "Pairwise stable networks in homogeneous societies with weak link externalities," European Journal of Operational Research, Elsevier, vol. 291(3), pages 1164-1179.
    • Handle: RePEc:eee:ejores:v:291:y:2021:i:3:p:1164-1179
    DOI: 10.1016/j.ejor.2020.09.025
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    Cited by:

    1. Peter-J. Jost, 2022. "Friend or foe? Co-opetition and entrepreneurial networking," Small Business Economics, Springer, vol. 59(3), pages 1043-1059, October.
    2. Nizar Allouch & A. Meca & K. Polotskaya, 2021. "The Bonacich Shapley centrality," Studies in Economics 2106, School of Economics, University of Kent.
    3. Mihaela Aurelia Tomescu & Lorentz Jäntschi & Doina Iulia Rotaru, 2021. "Figures of Graph Partitioning by Counting, Sequence and Layer Matrices," Mathematics, MDPI, vol. 9(12), pages 1-25, June.

    More about this item

    Keywords

    Network formation; Noncooperative games; Convexity; Strategic complements;
    All these keywords.

    JEL classification:

    • A14 - General Economics and Teaching - - General Economics - - - Sociology of Economics
    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • D85 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Network Formation

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