Abstract
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).
This research was supported in part by the National Nature Science Foundation of China (grant number 11971298, 71901145).
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Zhang, G., Shan, E., Qu, S. (2019). Characterizations of the Position Value for Hypergraph Communication Situations. In: Li, DF. (eds) Game Theory. EAGT 2019. Communications in Computer and Information Science, vol 1082. Springer, Singapore. https://doi.org/10.1007/978-981-15-0657-4_2
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DOI: https://doi.org/10.1007/978-981-15-0657-4_2
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