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The degree value for games with communication structure

Author

Listed:
  • Erfang Shan

    (Shanghai University)

  • Guang Zhang

    (Shanghai University
    Tilburg University)

  • Xiaokang Shan

    (Washington University in St. Louis)

Abstract

A new value concept, called degree value, is proposed by employing the degree game induced by an original game for hypergraph communication situations (including graph communication situations). We provide an axiomatic characterization of the degree value for arbitrary hypergraph communication situations by applying component efficiency and balanced conference contributions, which is a natural extension of balanced link contributions introduced in Slikker (Int J Game Theory 33:505–514, 2005) for graph communication situations. By comparing the degree value with the position value and the Myerson value, it is verified that the degree value is a new allocation rule that differs from both the Myerson value and the position value, and the degree value highlights the important role of the degree of a player in hypergraph communication situations. Particularly, in a uniform hypergraph communication situation, where every conference contains the same number of players, we show that the degree value coincides with the position value.

Suggested Citation

  • Erfang Shan & Guang Zhang & Xiaokang Shan, 2018. "The degree value for games with communication structure," International Journal of Game Theory, Springer;Game Theory Society, vol. 47(3), pages 857-871, September.
    • Handle: RePEc:spr:jogath:v:47:y:2018:i:3:d:10.1007_s00182-018-0631-0
    DOI: 10.1007/s00182-018-0631-0
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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.
    2. van den Nouweland, Anne & Borm, Peter & Tijs, Stef, 1992. "Allocation Rules for Hypergraph Communication Situations," International Journal of Game Theory, Springer;Game Theory Society, vol. 20(3), pages 255-268.
    3. Roger B. Myerson, 1977. "Graphs and Cooperation in Games," Mathematics of Operations Research, INFORMS, vol. 2(3), pages 225-229, August.
    4. E. Algaba & J. M. Bilbao & P. Borm & J. J. López, 2001. "The Myerson value for union stable structures," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 54(3), pages 359-371, December.
    5. André Casajus, 2007. "The position value is the Myerson value, in a sense," International Journal of Game Theory, Springer;Game Theory Society, vol. 36(1), pages 47-55, September.
    6. E. Algaba & J. M. Bilbao & P. Borm & J. J. López, 2000. "The position value for union stable systems," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 52(2), pages 221-236, November.
    7. 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.
    8. Shan, Erfang & Zhang, Guang & Dong, Yanxia, 2016. "Component-wise proportional solutions for communication graph games," Mathematical Social Sciences, Elsevier, vol. 81(C), pages 22-28.
    9. Takumi Kongo, 2010. "Difference between the position value and the Myerson value is due to the existence of coalition structures," International Journal of Game Theory, Springer;Game Theory Society, vol. 39(4), pages 669-675, October.
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    2. Xianghui Li & Yang Li, 2021. "On the Structural Stability of Values for Cooperative Games," Journal of Optimization Theory and Applications, Springer, vol. 189(3), pages 873-888, June.

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