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Degree Centrality, von Neumann-Morgenstern Expected Utility and Externalities in Networks

Author

Listed:
  • Rene’ van den Brink

    (Vrije Universiteit Amsterdam)

  • Agnieszka Rusinowska

    (University Paris 1 Pantheon-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.

Suggested Citation

  • Rene’ van den Brink & Agnieszka Rusinowska, 2023. "Degree Centrality, von Neumann-Morgenstern Expected Utility and Externalities in Networks," Tinbergen Institute Discussion Papers 23-061/II, Tinbergen Institute.
    • Handle: RePEc:tin:wpaper:20230061
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    References listed on IDEAS

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    More about this item

    Keywords

    weighted network; degree; centrality measure; externalities; neutrality to ordinary risk; expected utility function;
    All these keywords.

    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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