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Two classes of weighted values for coalition structures with extensions to level structures

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  • Besner, Manfred

Abstract

In this paper we introduce two new classes of weighted values for coalition structures with related extensions to level structures. The values of both classes coincide on given player sets with Harsanyi payoffs and match therefore adapted standard axioms for TU-values which are satisfied by these values. Characterizing elements of the values from the new classes are a new weighted proportionality within components property and a null player out property, but on different reduced games for each class. The values from the first class, we call them weighted Shapley alliance coalition structure values (weighted Shapley alliance levels values), satisfy the null player out property on usual reduced games. By contrast, the values from the second class, named as weighted Shapley collaboration coalition structure values (weighted Shapley collaboration levels values) have this property on new reduced games where a component decomposes in components of lower levels (these are singletons in a coalition structure) if one player of this component is removed from the game. The first class contains the Owen value (Shapley levels value) and the second class includes a new extension of the Shapley value to coalition structures (level structures) as a special case.

Suggested Citation

  • Besner, Manfred, 2018. "Two classes of weighted values for coalition structures with extensions to level structures," MPRA Paper 87742, University Library of Munich, Germany.
  • Handle: RePEc:pra:mprapa:87742
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    File URL: https://mpra.ub.uni-muenchen.de/88191/1/MPRA_paper_88191.pdf
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    References listed on IDEAS

    as
    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. Gómez-Rúa, María & Vidal-Puga, Juan, 2010. "The axiomatic approach to three values in games with coalition structure," European Journal of Operational Research, Elsevier, vol. 207(2), pages 795-806, December.
    4. 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.
    5. Jean J. M. Derks & Hans H. Haller, 1999. "Null Players Out? Linear Values For Games With Variable Supports," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 1(03n04), pages 301-314.
    6. Besner, Manfred, 2017. "Weighted Shapley levels values," MPRA Paper 82978, University Library of Munich, Germany.
    7. 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.
    8. Besner, Manfred, 2018. "The weighted Shapley support levels values," MPRA Paper 87617, University Library of Munich, Germany.
    9. AUMANN, Robert J. & DREZE, Jacques H., 1974. "Cooperative games with coalition structures," CORE Discussion Papers RP 217, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    10. 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.
    11. 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.
    12. 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.
    13. Nowak, A.S. & Radzik, T., 1995. "On axiomatizations of the weighted Shapley values," Games and Economic Behavior, Elsevier, vol. 8(2), pages 389-405.
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    More about this item

    Keywords

    Cooperative game · Weighted Shapley coalition structure values · Weighted Shapley levels values · Weighted proportionality within components · 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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