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Union Shapley Value: Quantifying Group Impact via Collective Removal

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  • Piotr Kk{e}pczy'nski
  • Oskar Skibski

Abstract

We perform a comprehensive analysis of extensions of the Shapley value to groups. We propose a new, natural extension called the Union Shapley Value, which assesses a group's contribution by examining the impact of its removal from the game. This intuition is formalized through two axiomatic characterizations, closely related to existing axiomatizations of the Shapley value. Furthermore, we characterize the class of group semivalues and identify a dual approach that measures synergy instead of the value of a coalition. Our analysis reveals a novel connection between several group values previously proposed in the literature.

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  • Piotr Kk{e}pczy'nski & Oskar Skibski, 2025. "Union Shapley Value: Quantifying Group Impact via Collective Removal," Papers 2505.21122, arXiv.org.
    • Handle: RePEc:arx:papers:2505.21122
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    References listed on IDEAS

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    1. Marc Roubens & Michel Grabisch, 1999. "An axiomatic approach to the concept of interaction among players in cooperative games," International Journal of Game Theory, Springer;Game Theory Society, vol. 28(4), pages 547-565.
    2. Roger B. Myerson, 1977. "Graphs and Cooperation in Games," Mathematics of Operations Research, INFORMS, vol. 2(3), pages 225-229, August.
    3. repec:dau:papers:123456789/4735 is not listed on IDEAS
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