Degree centrality, von Neumann–Morgenstern expected utility and externalities in networks
用合作博弈论连接社会网络中的中心性度量与冯·诺伊曼-摩根斯坦期望效用函数，发现仅由度（邻居数）决定的中心性度量类，并扩展到一般合作博弈。
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. • We consider network externalities from the connectedness of other positions. • We axiomatize network centrality measures that take account of such externalities. • We axiomatize these measures as von Neumann–Morgenstern utility functions. • Besides standard axioms, we only require anonymity and ordinary risk neutrality. • We extend this axiomatization to the more general cooperative games.