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Degree centrality, von Neumann–Morgenstern expected utility and externalities in networks

Author

Listed:
  • René van den Brink

    (VU - Vrije Universiteit Amsterdam [Amsterdam], Tinbergen Institute - Tinbergen Institute)

  • Agnieszka Rusinowska

    (PSE - Paris School of Economics - UP1 - Université Paris 1 Panthéon-Sorbonne - ENS-PSL - École normale supérieure - Paris - PSL - Université Paris Sciences et Lettres - EHESS - École des hautes études en sciences sociales - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement - ENPC - École nationale des ponts et chaussées - IP Paris - Institut Polytechnique de Paris, CES - Centre d'économie de la Sorbonne - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique, UP1 - Université Paris 1 Panthéon-Sorbonne)

Abstract

This paper aims to connect the social network literature on centrality measures with the economic literature on von Neumann-Morgenstern expected utility functions using cooperative game theory. The social network literature studies various concepts of network centrality, such as degree, betweenness, connectedness, and so on. This resulted in a great number of network centrality measures, each measuring centrality in a different way. In this paper, we aim to explore which centrality measures can be supported as von Neumann-Morgenstern expected utility functions, reflecting preferences over different network positions in different networks. Besides standard axioms on lotteries and preference relations, we consider neutrality to ordinary risk. We show that this leads to a class of centrality measures that is fully determined by the degrees (i.e. the numbers of neighbours) of the positions in a network. Although this allows for externalities, in the sense that the preferences of a position might depend on the way how other positions are connected, these externalities can be taken into account only by considering the degrees of the network positions. Besides bilateral networks, we extend our result to general cooperative TU-games to give a utility foundation of a class of TU-game solutions containing the Shapley value.
(This abstract was borrowed from another version of this item.)

Suggested Citation

  • René van den Brink & Agnieszka Rusinowska, 2024. "Degree centrality, von Neumann–Morgenstern expected utility and externalities in networks," Post-Print hal-05397810, HAL.
    • Handle: RePEc:hal:journl:hal-05397810
    DOI: 10.1016/j.ejor.2024.06.042
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    Cited by:

    1. is not listed on IDEAS
    2. Noriaki Matsushima & Mark J. Tremblay, 2024. "Network compatibility and incumbent pricing regimes," ISER Discussion Paper 1265, Institute of Social and Economic Research, The University of Osaka.
    3. Michele Aleandri & Francesco Ciardiello & Andrea Di Liddo, 2025. "Power in Sharing Networks with a priori Unions," Papers 2507.13272, arXiv.org.
    4. Michela Chessa, 2025. "Politics as A (Very) Complex System: A New Methodological Approach to Studying Fragmentation within a Council," GREDEG Working Papers 2025-16, Groupe de REcherche en Droit, Economie, Gestion (GREDEG CNRS), Université Côte d'Azur, France.

    More about this item

    JEL classification:

    • D85 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Network Formation
    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
    • C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics

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