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The Myerson Value and Superfluous Supports in Union Stable Systems

Author

Listed:
  • 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

This discussion paper resulted in a publication in the 'Journal of Optimization Theory and Applications' , 2012, 155, 650-668. 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.

Suggested Citation

  • 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.
    • Handle: RePEc:tin:wpaper:20110127
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    File URL: https://papers.tinbergen.nl/11127.pdf
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    References listed on IDEAS

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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. 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.
    3. 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.
    4. 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.
    5. Gilles, Robert P & Owen, Guillermo & van den Brink, Rene, 1992. "Games with Permission Structures: The Conjunctive Approach," International Journal of Game Theory, Springer;Game Theory Society, vol. 20(3), pages 277-293.
    6. 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.
    7. Roger B. Myerson, 1977. "Graphs and Cooperation in Games," Mathematics of Operations Research, INFORMS, vol. 2(3), pages 225-229, August.
    8. 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.
    9. René Brink & Gerard Laan & Vitaly Pruzhansky, 2011. "Harsanyi power solutions for graph-restricted games," International Journal of Game Theory, Springer;Game Theory Society, vol. 40(1), pages 87-110, February.
    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;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 54(3), pages 359-371, December.
    11. Potters, Jos & Reijnierse, Hans, 1995. "Gamma-Component Additive Games," International Journal of Game Theory, Springer;Game Theory Society, vol. 24(1), pages 49-56.
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    Cited by:

    1. 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.

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    More about this item

    Keywords

    Conference game; restricted game; union stable system; Myerson value; superfluous support property;
    All these keywords.

    JEL classification:

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

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