Weighted Shapley hierarchy levels values

Besner, Manfred (2018): Weighted Shapley hierarchy levels values.

Abstract

In this paper we present a new class of values for cooperative games with level structure. We use a multi-step proceeding, suggested first in Owen (1977), applied to the weighted Shapley values. Our first axiomatization is an generalisation of the axiomatization given in Gómez-Rúa and Vidal-Puga (2011), itselves an extension of a special case of an axiomatization given in Myerson (1980) and Hart and Mas-Colell (1989) respectively by efficiency and weighted balanced contributions. The second axiomatization is completely new and extends the axiomatization of the weighted Shapley values introduced in Hart and Mas-Colell (1989) by weighted standardness for two player games and consistency. As a corollary we obtain a new axiomatization of the Shapley levels value.

• Item Type: MPRA Paper
• Language: English
• Keywords: Cooperative game; Consistency; Level structure; (Weighted) Shapley (levels) value; Weighted balanced contributions
• Subjects: C - Mathematical and Quantitative Methods > C7 - Game Theory and Bargaining Theory; C - Mathematical and Quantitative Methods > C7 - Game Theory and Bargaining Theory > C71 - Cooperative Games

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