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The weighted Shapley support levels values

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  • Besner, Manfred

Abstract

This paper presents a new class of weighted values for level structures. The new values, called weighted Shapley support levels values, extend the weighted Shapley values to level structures and contain the Shapley levels value (Winter, 1989) as a special case. Since a level structure with only two levels coincides with a coalition structure we obtain, as a side effect, also new axiomatizations of weighted coalition structure values, presented in Levy and McLean (1989).

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  • Besner, Manfred, 2018. "The weighted Shapley support levels values," MPRA Paper 87617, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:87617
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    References listed on IDEAS

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    1. McLean, Richard P, 1991. "Random Order Coalition Structure Values," International Journal of Game Theory, Springer;Game Theory Society, vol. 20(2), pages 109-127.
    2. Levy, Anat & Mclean, Richard P., 1989. "Weighted coalition structure values," Games and Economic Behavior, Elsevier, vol. 1(3), pages 234-249, September.
    3. Vidal-Puga, Juan, 2012. "The Harsanyi paradox and the “right to talk” in bargaining among coalitions," Mathematical Social Sciences, Elsevier, vol. 64(3), pages 214-224.
    4. M. Álvarez-Mozos & R. Brink & G. Laan & O. Tejada, 2017. "From hierarchies to levels: new solutions for games with hierarchical structure," International Journal of Game Theory, Springer;Game Theory Society, vol. 46(4), pages 1089-1113, November.
    5. André Casajus, 2010. "Another characterization of the Owen value without the additivity axiom," Theory and Decision, Springer, vol. 69(4), pages 523-536, October.
    6. AUMANN, Robert J. & DREZE, Jacques H., 1974. "Cooperative games with coalition structures," LIDAM Reprints CORE 217, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    7. Jean Derks & Hans Haller & Hans Peters, 2000. "The selectope for cooperative games," International Journal of Game Theory, Springer;Game Theory Society, vol. 29(1), pages 23-38.
    8. Nowak, A.S. & Radzik, T., 1995. "On axiomatizations of the weighted Shapley values," Games and Economic Behavior, Elsevier, vol. 8(2), pages 389-405.
    9. Anna Khmelnitskaya & Elena Yanovskaya, 2007. "Owen coalitional value without additivity axiom," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 66(2), pages 255-261, October.
    10. Winter, Eyal, 1989. "A Value for Cooperative Games with Levels Structure of Cooperation," International Journal of Game Theory, Springer;Game Theory Society, vol. 18(2), pages 227-240.
    11. Besner, Manfred, 2017. "Weighted Shapley levels values," MPRA Paper 82978, University Library of Munich, Germany.
    12. Calvo, Emilio & Javier Lasaga, J. & Winter, Eyal, 1996. "The principle of balanced contributions and hierarchies of cooperation," Mathematical Social Sciences, Elsevier, vol. 31(3), pages 171-182, June.
    13. María Gómez-Rúa & Juan Vidal-Puga, 2011. "Balanced per capita contributions and level structure of cooperation," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 19(1), pages 167-176, July.
    14. Chun, Youngsub, 1989. "A new axiomatization of the shapley value," Games and Economic Behavior, Elsevier, vol. 1(2), pages 119-130, June.
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    Cited by:

    1. Besner, Manfred, 2018. "Weighted Shapley hierarchy levels values," MPRA Paper 88160, University Library of Munich, Germany.
    2. Besner, Manfred, 2018. "Two classes of weighted values for coalition structures with extensions to level structures," MPRA Paper 87742, University Library of Munich, Germany.

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    More about this item

    Keywords

    Cooperative game · Level structure · (Weighted) Shapley (levels) value · Weighted proportionality · Harsanyi set · Dividends;

    JEL classification:

    • C70 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - General
    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games

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