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Proportional Shapley levels values

Besner, Manfred (2018): Proportional Shapley levels values.

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Abstract

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.

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