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The Myerson Value and Superfluous Supports in Union Stable Systems

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Author Info

  • Encarnacion Algaba

    (University of Sevilla)

  • Jesus Mario Bilbao

    (University of Sevilla)

  • Rene van den Brink

    (VU University Amsterdam)

  • Jorge J. Lopez

    (University of Sevilla)

Abstract

Cooperative games with partial cooperation cover a wider rank of real world situations than the classic model of cooperative games where every subset of a set of agents can form a coalition to execute the game. In this paper, the set of feasible coalitions which models the partial cooperation will be given by a union stable system. These systems contain, as particular cases, the communication situations and the permission structures, which are well-known both from a theoretical and applied point of view. Moreover, union stable systems are a natural framework for many other economic situations that arise in practice and which can not be modelled by these subsystems. In this paper, the goal is to make clear that there exists a close relationship between the Myerson value and the so-called conference game which player set consists of the supports of the union stable system. For that, we first analyze the relation between the restricted game and the conference game to establish later which effects a union stable system has on certain desirable properties of these games. Using the superfluous support property, defined through the conference game, new characterizations for the Myerson value are given in this context.

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Bibliographic Info

Paper provided by Tinbergen Institute in its series Tinbergen Institute Discussion Papers with number 11-127/1.

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Date of creation: 08 Sep 2011
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Handle: RePEc:dgr:uvatin:20110127

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Web page: http://www.tinbergen.nl

Related research

Keywords: Conference game; restricted game; union stable system; Myerson value; superfluous support property;

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References

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  1. Potters, Jos & Reijnierse, Hans, 1995. "Gamma-Component Additive Games," International Journal of Game Theory, Springer, vol. 24(1), pages 49-56.
  2. Nouweland, C.G.A.M. van den & Borm, P.E.M., 1991. "On the convexity of communication games," Open Access publications from Tilburg University urn:nbn:nl:ui:12-146634, Tilburg University.
  3. René Brink & Gerard Laan & Vitaly Pruzhansky, 2011. "Harsanyi power solutions for graph-restricted games," International Journal of Game Theory, Springer, vol. 40(1), pages 87-110, February.
  4. repec:hal:cesptp:hal-00625336 is not listed on IDEAS
  5. E. Algaba & J. M. Bilbao & J. J. López, 2004. "The position value in communication structures," Computational Statistics, Springer, vol. 59(3), pages 465-477, 07.
  6. Gilles, R.P. & Owen, G. & Brink, J.R. van den, 1991. "Games with permission structures: The conjunctive approach," Discussion Paper 1991-14, Tilburg University, Center for Economic Research.
  7. E. Algaba & J. M. Bilbao & P. Borm & J. J. López, 2000. "The position value for union stable systems," Computational Statistics, Springer, vol. 52(2), pages 221-236, November.
  8. RenÊ van den Brink, 1997. "An Axiomatization of the Disjunctive Permission Value for Games with a Permission Structure," International Journal of Game Theory, Springer, vol. 26(1), pages 27-43.
  9. van den Nouweland, Anne & Borm, Peter & Tijs, Stef, 1992. "Allocation Rules for Hypergraph Communication Situations," International Journal of Game Theory, Springer, vol. 20(3), pages 255-68.
  10. E. Algaba & J. M. Bilbao & P. Borm & J. J. López, 2001. "The Myerson value for union stable structures," Mathematical Methods of Operations Research, Springer, vol. 54(3), pages 359-371, December.
  11. Borm, P.E.M. & Owen, G. & Tijs, S.H., 1992. "On the position value for communication situations," Open Access publications from Tilburg University urn:nbn:nl:ui:12-154855, Tilburg University.
  12. Borm, P.E.M. & Algaba, A. & Bilbao, J.M. & Lopez, J., 2002. "The Myerson value for union stable systems," Open Access publications from Tilburg University urn:nbn:nl:ui:12-90189, Tilburg University.
  13. Encarnacion Algaba & Jesus Mario Bilbao & Rene van den Brink, 2011. "Harsanyi Power Solutions for Games on Union Stable Systems," Tinbergen Institute Discussion Papers 11-182/1, Tinbergen Institute.
  14. René van den Brink, 2006. "On Hierarchies and Communication," Tinbergen Institute Discussion Papers 06-056/1, Tinbergen Institute.
  15. 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.
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Cited by:
  1. Encarnacion Algaba & Jesus Mario Bilbao & Rene van den Brink, 2011. "Harsanyi Power Solutions for Games on Union Stable Systems," Tinbergen Institute Discussion Papers 11-182/1, Tinbergen Institute.

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