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Cooperative Games on Accessible Union Stable Systems

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  • Encarnación Algaba

    (Escuela Técnica Superior de Ingenierá, Sevilla, Spain)

  • René van den Brink

    (VU University Amsterdam)

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    Abstract

    Agents participating in different kind of organizations, usually take different positions in some relational structure. The aim of this paper is to introduce a new framework taking into account both communication and hierachical features derived from this participation. In fact, this new set or network structure unifies and generalizes well-known models from the literature, such as communication networks and hierarchies. We introduce and analyze accessible union stable systems where union stability reflects the communication network and accessibility describes the hierarchy. Particular cases of these new structures are the sets of connected coalitions in a communication graph, antimatroids (and therefore also sets of feasible coalitions in permission structures) and augmenting systems which have numerous applications in the literature. We give special attention to th e class of cycle-free accessible union stable systems. We also consider cooperative games with restricted cooperation where the set of feasible coalitions is an accessible union stable system, and provide an axiomatization of an extension of the Shapley value to this class of games.

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    Bibliographic Info

    Paper provided by Tinbergen Institute in its series Tinbergen Institute Discussion Papers with number 13-207/II.

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    Date of creation: 19 Dec 2013
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    Handle: RePEc:dgr:uvatin:20130207

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

    Related research

    Keywords: union stable system; accessibility; cooperative TU-game; Shapley value;

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    References

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    1. Gilles, Robert P & Owen, Guillermo & van den Brink, Rene, 1992. "Games with Permission Structures: The Conjunctive Approach," International Journal of Game Theory, Springer, Springer, vol. 20(3), pages 277-93.
    2. Le Breton, M & Owen, G & Weber, S, 1992. "Strongly Balanced Cooperative Games," International Journal of Game Theory, Springer, Springer, vol. 20(4), pages 419-27.
    3. Demange, Gabrielle, 1994. "Intermediate preferences and stable coalition structures," Journal of Mathematical Economics, Elsevier, vol. 23(1), pages 45-58, January.
    4. Matthew O. Jackson & Asher Wolinsky, 1994. "A Strategic Model of Social and Economic Networks," Discussion Papers, Northwestern University, Center for Mathematical Studies in Economics and Management Science 1098, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    5. E. Algaba & J. M. Bilbao & R. van den Brink & A. Jiménez-Losada, 2003. "Axiomatizations of the Shapley value for cooperative games on antimatroids," Computational Statistics, Springer, Springer, vol. 57(1), pages 49-65, 04.
    6. René Brink, 2012. "On hierarchies and communication," Social Choice and Welfare, Springer, Springer, vol. 39(4), pages 721-735, October.
    7. Algaba, E. & Bilbao, J.M. & Borm, P.E.M. & Lopez, J.J., 1998. "The position value for union stable systems," Research Memorandum, Tilburg University, Faculty of Economics and Business Administration 768, Tilburg University, Faculty of Economics and Business Administration.
    8. E. Algaba & J. M. Bilbao & P. Borm & J. J. López, 2001. "The Myerson value for union stable structures," Mathematical Methods of Operations Research, Springer, Springer, vol. 54(3), pages 359-371, December.
    9. Hamiache, Gerard, 1999. "A Value with Incomplete Communication," Games and Economic Behavior, Elsevier, Elsevier, vol. 26(1), pages 59-78, January.
    10. van den Brink, Rene & Gilles, Robert P., 1996. "Axiomatizations of the Conjunctive Permission Value for Games with Permission Structures," Games and Economic Behavior, Elsevier, Elsevier, vol. 12(1), pages 113-126, January.
    11. Curiel, I. & Potters, J.A.M. & Rajendra Prasad, V. & Tijs, S.H. & Veltman, B., 1994. "Sequencing and cooperation," Open Access publications from Tilburg University urn:nbn:nl:ui:12-154192, Tilburg University.
    12. 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.
    13. S. C. Littlechild & G. Owen, 1973. "A Simple Expression for the Shapley Value in a Special Case," Management Science, INFORMS, INFORMS, vol. 20(3), pages 370-372, November.
    14. Algaba, A. & Bilbao, J.M. & Brink, J.R. van den & Jiménez-Losada, A., 2000. "Cooperative Games on Antimatroids," Discussion Paper, Tilburg University, Center for Economic Research 2000-124, Tilburg University, Center for Economic Research.
    15. Matthew O. Jackson & Tomas Rodriguez-Barraquer & Xu Tan, 2012. "Social Capital and Social Quilts: Network Patterns of Favor Exchange," American Economic Review, American Economic Association, American Economic Association, vol. 102(5), pages 1857-97, August.
    16. Gabrielle Demange, 2004. "On group stability in hierarchies and networks," Post-Print, HAL halshs-00581662, HAL.
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