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Frontiers of Dynamic Games pp 237–250Cite as

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The Position Value and the Myerson Value for Hypergraph Communication Situations

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Part of the book series: Static & Dynamic Game Theory: Foundations & Applications ((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.

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Acknowledgements

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

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Authors and Affiliations

  1. School of Management, Shanghai University, Shanghai, People’s Republic of China

    Erfang Shan & Guang Zhang

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  1. Erfang Shan
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  2. Guang Zhang
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Correspondence to Erfang Shan .

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Editors and Affiliations

  1. St. Petersburg State University, St. Petersburg, Russia

    Leon A. Petrosyan

  2. Institute of Applied Mathematical Research, Karelian Research Center of RAS, Petrozavodsk, Russia

    Vladimir V. Mazalov

  3. Graduate School of Management, St. Petersburg State University, St. Petersburg, Russia

    Nikolay A. Zenkevich

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Shan, E., Zhang, G. (2018). The Position Value and the Myerson Value for Hypergraph Communication Situations. In: Petrosyan, L., Mazalov, V., Zenkevich, N. (eds) Frontiers of Dynamic Games. Static & Dynamic Game Theory: Foundations & Applications. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-92988-0_14

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