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Weighted Shapley levels values

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  • Besner, Manfred

Abstract

This paper presents a collection of four different classes of weighted Shapley levels values. All classes contain generalisations of the weighted Shapley values to cooperative games with a level structure. The first class is an upgrade of the weighted Shapley levels value in Gómez-Rúa and Vidal-Puga (2011), who use the size of components as weights. The following classes contain payoff vectors from the Harsanyi set. Hence they satisfy the dummy axiom, in contrary to the values in the first class in general. The second class contains extensions of the McLean weighted coalition structure values (Dragan, 1992; Levy and McLean, 1989; McLean, 1991). The first two classes satisfy the level game property (the payoff to all players of a component sum up to the payoff to the component in a game where components are the players) and the last two classes meet a null player out property. As a special case, the first three classes include the Shapley levels value and the last class contains a new extension of the Shapley value.

Suggested Citation

  • Besner, Manfred, 2017. "Weighted Shapley levels values," MPRA Paper 82978, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:82978
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    File URL: https://mpra.ub.uni-muenchen.de/83155/1/MPRA_paper_83155.pdf
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    References listed on IDEAS

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    Cited by:

    1. Besner, Manfred, 2018. "The weighted Shapley support levels values," MPRA Paper 87617, 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;
    All these keywords.

    JEL classification:

    • C7 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory
    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games

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