Characterizations of the Position Value for Hypergraph Communication Situations
We characterize the position value for arbitrary hypergraph communication situations. The position value is first presented by the Shapley value of the uniform hyperlink game or the k-augmented uniform hyperlink game, which are obtained from a given hypergraph communication situation. These results generalize the non-axiomatic characterization of the position value from communication situations in Kongo (2010) (Int J Game Theory (2010) 39: 669–675) to hypergraph communication situations. Based on the non-axiomatic characterizations, we further provide an axiomatic characterization of the position value for arbitrary hypergraph communication situations by employing component efficiency and a new property, named partial balanced conference contributions. Partial balanced conference contributions is developed from balanced link contributions in Slikker (2005) (Int J Game Theory (2005) 33: 505–514).
KeywordsHypergraph communication situation Position value Characterization
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