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

René van den Brink () and Agnieszka Rusinowska ()
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René van den Brink: VU University Amsterdam and Tinbergen Institute
Agnieszka Rusinowska: CES - Centre d'économie de la Sorbonne - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique, CNRS - Centre National de la Recherche Scientifique, UP1 - Université Paris 1 Panthéon-Sorbonne, 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 - ENPC - École nationale des ponts et chaussées - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement

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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.

Keywords: group decisions and negotiations; weighted graph; degree centrality; von Neumann-Morgenstern expected utility function; cooperative game (search for similar items in EconPapers)
Date: 2024-12
New Economics Papers: this item is included in nep-gth, nep-net and nep-upt
Note: View the original document on HAL open archive server: https://shs.hal.science/halshs-04188289v2
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Published in European Journal of Operational Research, 2024, 319 (2), pp.669-677. ⟨10.1016/j.ejor.2024.06.042⟩

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Persistent link: https://EconPapers.repec.org/RePEc:hal:pseptp:halshs-04188289

DOI: 10.1016/j.ejor.2024.06.042

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