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Solutions without dummy axiom for TU cooperative games

Author

Listed:
  • Francisco Sanchez-Sanchez

    () (CIMAT)

  • Ruben Juarez

    () (Rice University)

  • Luis Hernandez-Lamoneda

    () (CIMAT)

Abstract

In this paper we study an expression for all additive, symmetric and efficient solutions, i.e., the set of axioms that traditionally are used to characterize the Shapley value except for the dummy axiom. Also, we obtain an expression for this kind of solutions by including the self duality axiom. These expressions allow us to give an alternative formula for the consensus value, the generalized consensus value and the solidarity solution. Furthermore, we introduce a new axiom called coalitional independence which replaces the symmetry axiom and use it to get similar results.

Suggested Citation

  • Francisco Sanchez-Sanchez & Ruben Juarez & Luis Hernandez-Lamoneda, 2008. "Solutions without dummy axiom for TU cooperative games," Economics Bulletin, AccessEcon, vol. 3(1), pages 1-9.
  • Handle: RePEc:ebl:ecbull:eb-07c70040
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    References listed on IDEAS

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    1. Yuan Ju & Peter Borm & Pieter Ruys, 2007. "The consensus value: a new solution concept for cooperative games," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 28(4), pages 685-703, June.
    2. L. Hernández-Lamoneda & R. Juárez & F. Sánchez-Sánchez, 2007. "Dissection of solutions in cooperative game theory using representation techniques," International Journal of Game Theory, Springer;Game Theory Society, vol. 35(3), pages 395-426, February.
    3. Ruiz, Luis M & Valenciano, Federico & Zarzuelo, Jose M, 1996. "The Least Square Prenucleolus and the Least Square Nucleolus. Two Values for TU Games Based on the Excess Vector," International Journal of Game Theory, Springer;Game Theory Society, vol. 25(1), pages 113-134.
    4. Nowak, Andrzej S & Radzik, Tadeusz, 1994. "A Solidarity Value for n-Person Transferable Utility Games," International Journal of Game Theory, Springer;Game Theory Society, vol. 23(1), pages 43-48.
    5. Ruiz, Luis M. & Valenciano, Federico & Zarzuelo, Jose M., 1998. "The Family of Least Square Values for Transferable Utility Games," Games and Economic Behavior, Elsevier, vol. 24(1-2), pages 109-130, July.
    Full references (including those not matched with items on IDEAS)

    Citations

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    Cited by:

    1. Emilio Calvo & Esther Gutiérrez-López, 2015. "The value in games with restricted cooperation," Discussion Papers in Economic Behaviour 0115, University of Valencia, ERI-CES.
    2. Chameni Nembua, Célestin & Demsou, Themoi, 2013. "Ordinal equivalence of values and Pigou-Dalton transfers in TU-games," MPRA Paper 44895, University Library of Munich, Germany, revised 09 Mar 2013.
    3. Célestin Chameni Nembua & Nicolas Gabriel Andjiga, 2008. "Linear, efficient and symmetric values for TU-games," Economics Bulletin, AccessEcon, vol. 3(71), pages 1-10.
    4. Nembua Célestin, Chameni & Wendji Clovis, Miamo, 2017. "On some decisive players for linear efficient and symmetric values in cooperative games with transferable utility," MPRA Paper 83670, University Library of Munich, Germany, revised 2017.

    More about this item

    Keywords

    axiomatic characterization;

    JEL classification:

    • C7 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory
    • C7 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory

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