The class of ASN-position values

This paper introduces a class of cooperative allocation rules for TU-games with a network structure that account for an agent’s centrality in the network. In contrast to existing centrality measures, this approach analyzes the consequences of tie failure (rather than node failure). Though not directly applied to the centrality issue, tie failures are the idea underlying the Position value (the Shapley value of the arc-game). In contrast, we allow for a whole class of allocation rules as a basis since the Shapley approach might be unreasonable in political applications, especially in networks with incompatibilities. Requiring additivity (A), equal treatment of equals (Symmetry S), and irrelevance of unproductive agents (nullplayer irrelevance N) for the underlying basis, we define the class of ASN-position values and provide axiomatic characterizations. To emphasize the crucial role of links, we refine this class to multiplicative ASN-position values and provide a monotonicity result with respect to links. We apply our approach to the case of the 2001 state parliament elections in Hamburg, Germany to use our allocation rule as a power index and further provide an example where we use our approach as a centrality measure to identify top key nodes. In both applications, the position value taking the Banzhaf value as a basis turns out to be more convincing than the Shapley-based approach.