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The Myerson value for union stable structures

Author

Listed:
  • E. Algaba
  • J. M. Bilbao
  • P. Borm
  • 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. These combinatorial structures have a direct relationship with graph communication situations and conference structures à la Myerson. Characterizations of the Myerson value in this context are provided using the concept of basis for union stable systems. Moreover, TU-games restricted by union stable systems generalizes graph-restricted games and games with permission structures. Copyright Springer-Verlag Berlin Heidelberg 2001

Suggested Citation

  • 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.
  • Handle: RePEc:spr:mathme:v:54:y:2001:i:3:p:359-371
    DOI: 10.1007/s001860100159
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    Citations

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    Cited by:

    1. René Brink, 2012. "On hierarchies and communication," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 39(4), pages 721-735, October.
    2. René van den Brink, 2017. "Games with a Permission Structure: a survey on generalizations and applications," Tinbergen Institute Discussion Papers 17-016/II, Tinbergen Institute.
    3. repec:hal:journl:hal-00625336 is not listed on IDEAS
    4. Koshevoy, Gleb & Talman, Dolf, 2014. "Solution concepts for games with general coalitional structure," Mathematical Social Sciences, Elsevier, vol. 68(C), pages 19-30.
    5. Béal, Sylvain & Rémila, Eric & Solal, Philippe, 2012. "Weighted component fairness for forest games," Mathematical Social Sciences, Elsevier, vol. 64(2), pages 144-151.
    6. Caulier, Jean-François & Mauleon, Ana & Vannetelbosch, Vincent, 2015. "Allocation rules for coalitional network games," Mathematical Social Sciences, Elsevier, vol. 78(C), pages 80-88.
    7. 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.
    8. Emilio Calvo & Esther Gutiérrez-López, 2015. "The value in games with restricted cooperation," Discussion Papers in Economic Behaviour 0115, University of Valencia, ERI-CES.
    9. Faigle, U. & Grabisch, M. & Heyne, M., 2010. "Monge extensions of cooperation and communication structures," European Journal of Operational Research, Elsevier, vol. 206(1), pages 104-110, October.
    10. Koshevoy, G.A. & Suzuki, T. & Talman, A.J.J., 2013. "Solutions For Games With General Coalitional Structure And Choice Sets," Discussion Paper 2013-012, Tilburg University, Center for Economic Research.
    11. 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.
    12. René Brink & Chris Dietz, 2014. "Games with a local permission structure: separation of authority and value generation," Theory and Decision, Springer, vol. 76(3), pages 343-361, March.
    13. repec:spr:compst:v:74:y:2011:i:3:p:427-443 is not listed on IDEAS
    14. 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.
    15. Newton, Jonathan, 2012. "Coalitional stochastic stability," Games and Economic Behavior, Elsevier, vol. 75(2), pages 842-854.
    16. González–Arangüena, E. & Manuel, C. & Owen, G. & del Pozo, M., 2017. "The within groups and the between groups Myerson values," European Journal of Operational Research, Elsevier, vol. 257(2), pages 586-600.
    17. Takashi Ui & Hiroyuki Kojima & Atsushi Kajii, 2011. "The Myerson value for complete coalition structures," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 74(3), pages 427-443, December.
    18. Selcuk, O. & Talman, A.J.J., 2013. "Games With General Coalitional Structure," Discussion Paper 2013-002, Tilburg University, Center for Economic Research.
    19. Koshevoy, G.A. & Talman, A.J.J., 2011. "Solution Concepts for Games with General Coalitional Structure (Replaces CentER DP 2011-025)," Discussion Paper 2011-119, Tilburg University, Center for Economic Research.

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