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Proportional Shapley levels values


  • Besner, Manfred


The proportional Shapley value (Besner 2016; Béal et al. 2017; Gangolly 1981) is an proportional counterpart to the Shapley value (Shapley 1953b) in cooperative games. As shown in Besner (2017a), the proportional Shapley value is a convincing non-linear alternative, especially in cost allocation, if the stand alone worths of the players are plausible weights. To enable similar properties for cooperative games with a level structure, we generalize this value. Therefore we adapt the proceeding applied to the weighted Shapley values in Besner (2017b). We present, analogous to the four classes of weighted Shapley levels values in Besner (2017b), four different values, the proportional Shapley hierarchy levels value, the proportional Shapley support levels value, the proportional Shapley alliance levels value and the proportional Shapley collaboration levels value, respectively.

Suggested Citation

  • Besner, Manfred, 2018. "Proportional Shapley levels values," MPRA Paper 87120, University Library of Munich, Germany.
  • Handle: RePEc:pra:mprapa:87120

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    More about this item


    Cooperative game · Level structure · (Proportional) Shapley (levels) value · Proportionality · Component substitution · 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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