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Efficiency and stability in the connections model with heterogeneous node

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  • Olaizola, Norma
  • Valenciano, Federico

Abstract

This paper studies the connections model (Jackson and Wolinsky, 1996) when nodes may have different values. It is shown that efficiency is reached by a strongly hierarchical structure that we call strong NSG-networks: Nested Split Graph networks where the hierarchy or ranking of nodes inherent in any such network is consistent with the rank of nodes according to their value, perhaps leaving some of the nodes with the lowest values disconnected. A simple algorithm is provided for calculating these efficient networks. We also introduce a natural extension of pairwise stability assuming that players are allowed to agree on how the cost of each link is split and prove that stability in this sense for connected strong NSG-networks entails efficiency.

Suggested Citation

  • Olaizola, Norma & Valenciano, Federico, 2021. "Efficiency and stability in the connections model with heterogeneous node," MPRA Paper 107797, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:107797
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    Cited by:

    1. Olaizola, Norma & Valenciano, Federico, 2022. "Efficient networks in connections models with heterogeneous nodes and links," MPRA Paper 114884, University Library of Munich, Germany.
    2. Olaizola, Norma & Valenciano, Federico, 2024. "Core–periphery and nested networks emerging from a simple model of network formation," Mathematical Social Sciences, Elsevier, vol. 129(C), pages 42-51.
    3. Norma Olaizola & Federico Valenciano, 2023. "A connections model with decreasing returns link-formation technology," SERIEs: Journal of the Spanish Economic Association, Springer;Spanish Economic Association, vol. 14(1), pages 31-61, March.
    4. Banchongsan Charoensook, 2022. "A Characterization of Nonminimal Nash Networks in Two-way Flow Model," Annals of Economics and Finance, Society for AEF, vol. 23(2), pages 329-340, November.

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    More about this item

    Keywords

    Networks; Connections model; Heterogeneity; Efficiency; Stability.;
    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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