The position value and the structures of graphs

摘要

The position value is an allocation rule based on the Shapley value of the link game from the original communication situation, in which cooperation is restricted by a graph. In the link games, feasible coalitions are connected but their structures are ignored. We introduce structure functions to describe the structures of connected sets, and generalize the link game and the position value to the setting with local structures. We modify an axiomatic characterization for the position value by Slikker to the generalized position value by component efficiency and Balanced link contributions on local structures.