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

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.