## 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.

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.

Original language | English |
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Publisher | Tinbergen Insttute |

Number of pages | 20 |

Publication status | Published - 2023 |

### Publication series

Name | TI Discussion Paper Series |
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Volume | 2023-061/II |