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Decomposition of network communication games

Author

Listed:
  • Bas Dietzenbacher

    (Tilburg University)

  • Peter Borm

    (Tilburg University)

  • Ruud Hendrickx

    (Tilburg University)

Abstract

Using network control structures, this paper introduces a general class of network communication games and studies their decomposition into unanimity games. We obtain a relation between the dividends in any network communication game and its underlying transferable utility game, which depends on the structure of the communication network. Moreover, we introduce a new class of network control values which contains both the Myerson value and the position value. The decomposition results are used to explicitly express these values in terms of dividends.

Suggested Citation

  • Bas Dietzenbacher & Peter Borm & Ruud Hendrickx, 2017. "Decomposition of network communication games," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 85(3), pages 407-423, June.
    • Handle: RePEc:spr:mathme:v:85:y:2017:i:3:d:10.1007_s00186-017-0576-2
    DOI: 10.1007/s00186-017-0576-2
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    1. 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.
    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. 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.
    4. Roger B. Myerson, 1977. "Graphs and Cooperation in Games," Mathematics of Operations Research, INFORMS, vol. 2(3), pages 225-229, August.
    5. E. Algaba & J. M. Bilbao & J. J. López, 2004. "The position value in communication structures," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 59(3), pages 465-477, July.
    6. 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.
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    Cited by:

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    More about this item

    Keywords

    Network control structures; Network communication games; Decomposition theory; Network control values; Myerson value; Position value;
    All these keywords.

    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games

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