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The position value in communication structures

Author

Listed:
  • E. Algaba
  • J. M. Bilbao
  • J. J. López

Abstract

We study cooperation structures with the following property: given any two feasible coalitions with non-empty intersection, its union is a feasible coalition again. TU-games restricted by union stable systems generalize graph-restricted games and games with permission structures. A study about the differences between the position value in union stable systems and hypergraph communication situations is given. Moreover, some computational aspects related to position value in union stable systems are discussed. Copyright Springer-Verlag 2004

Suggested Citation

  • 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.
    • Handle: RePEc:spr:mathme:v:59:y:2004:i:3:p:465-477
    DOI: 10.1007/s001860400343
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    Citations

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    Cited by:

    1. Encarnación Algaba & Stefano Moretti & Eric Rémila & Philippe Solal, 2021. "Lexicographic solutions for coalitional rankings," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 57(4), pages 817-849, November.
    2. Florian Navarro, 2019. "Necessary players, Myerson fairness and the equal treatment of equals," Annals of Operations Research, Springer, vol. 280(1), pages 111-119, September.
    3. Encarnaciön Algaba & Sylvain Béal & Eric Rémila & Phillippe Solal, 2018. "Harsanyi power solutions for cooperative games on voting structures," Working Papers 2018-05, CRESE.
    4. E. Algaba & J. Bilbao & R. Brink, 2015. "Harsanyi power solutions for games on union stable systems," Annals of Operations Research, Springer, vol. 225(1), pages 27-44, February.
    5. 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.
    6. E. Algaba & J. M. Bilbao & R. Brink & J. J. López, 2012. "The Myerson Value and Superfluous Supports in Union Stable Systems," Journal of Optimization Theory and Applications, Springer, vol. 155(2), pages 650-668, November.
    7. Encarnacion Algaba & Rene van den Brink, 2019. "The Shapley Value and Games with Hierarchies," Tinbergen Institute Discussion Papers 19-064/II, Tinbergen Institute.
    8. Encarnacion Algaba & Jesus Mario Bilbao & Rene van den Brink & Jorge J. Lopez, 2011. "The Myerson Value and Superfluous Supports in Union Stable Systems," Tinbergen Institute Discussion Papers 11-127/1, Tinbergen Institute.
    9. Encarnacion Algaba & Rene van den Brink, 2021. "Networks, Communication and Hierarchy: Applications to Cooperative Games," Tinbergen Institute Discussion Papers 21-019/IV, Tinbergen Institute.
    10. Encarnación Algaba & René Brink & Chris Dietz, 2018. "Network Structures with Hierarchy and Communication," Journal of Optimization Theory and Applications, Springer, vol. 179(1), pages 265-282, October.

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