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The Position Value and the Myerson Value for Hypergraph Communication Situations

  • Erfang ShanEmail author
  • Guang Zhang
Chapter
Part of the Static & Dynamic Game Theory: Foundations & Applications book series (SDGTFA)

Abstract

We characterize the position value and the Myerson value for uniform hypergraph communication situations by employing the “incidence graph game” and the “link-hypergraph game” which are induced by the original hypergraph communication situations. The incidence graph game and link-hypergraph game are defined on the “incidence graph” and the “link-hypergraph”, respectively, obtained from the original hypergraph. Using the above tools, we represent the position value by the Shapley value of the incidence graph game and the Myerson value of the link-hypergraph game for uniform hypergraph communication situations, respectively. Also, we represent the Myerson value by the Owen value or the two-step Shapley value of the incidence graph game with a coalition structure for hypergraph communication situations.

Notes

Acknowledgements

This research was supported in part by the National Nature Science Foundation of China (grant number 11571222).

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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.School of ManagementShanghai UniversityShanghaiPeople’s Republic of China

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