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A new value for communication situations

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Listed:
  • Daniel Li Li

    (Shanghai Business School)

  • Erfang Shan

    (Shanghai University)

Abstract

A communication situation (N, v, H) consists of a cooperative game (N, v) and a communication hypergraph (N, H), for which the Myerson value and the position value are well-known allocation rules. The value defined in this paper treats links in H as imaginal players, for which we define a bipartite graph between N and H according to the structure given by H, and propose an allocation rule called the bipartite value. This value assigns payoff to each player with two parts: as a player and as a member in links. A characterization of the bipartite value is given.

Suggested Citation

  • Daniel Li Li & Erfang Shan, 2024. "A new value for communication situations," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 100(2), pages 535-551, October.
    • Handle: RePEc:spr:mathme:v:100:y:2024:i:2:d:10.1007_s00186-024-00873-0
    DOI: 10.1007/s00186-024-00873-0
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    References listed on IDEAS

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    1. Marco Slikker, 2005. "A characterization of the position value," International Journal of Game Theory, Springer;Game Theory Society, vol. 33(4), pages 505-514, November.
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    4. Borm, P.E.M. & Owen, G. & Tijs, S.H., 1992. "On the position value for communication situations," Other publications TiSEM 5a8473e4-1df7-42df-ad53-f, Tilburg University, School of Economics and Management.
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    7. Roger B. Myerson, 1977. "Graphs and Cooperation in Games," Mathematics of Operations Research, INFORMS, vol. 2(3), pages 225-229, August.
    8. Liying Kang & Anna Khmelnitskaya & Erfang Shan & Dolf Talman & Guang Zhang, 2021. "The average tree value for hypergraph games," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 94(3), pages 437-460, December.
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