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Decomposition of solutions and the Shapley value

  • We suggest foundations for the Shapley value and for the naïve solution, which assigns to any player the difference between the worth of the grand coalition and its worth after this player left the game. To this end, we introduce the decomposition of solutions for cooperative games with transferable utility. A decomposer of a solution is another solution that splits the former into a direct part and an indirect part. While the direct part (the decomposer) measures a player's contribution in a game as such, the indirect part indicates how she affects the other players' direct contributions by leaving the game. The Shapley value turns out to be unique decomposable decomposer of the naïve solution.

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Document Type:Article
Author:André CasajusORCiD, Frank HuettnerORCiD
Chairs and Professorships:Chair of Economics and Information Systems
Parent Title (English):Games and economic behavior
Issue:March 2018
Year of Completion:2018
First Page:37
Last Page:48
Tag:Balanced contributions; Consistency; Decomposition; Higher-order contributions; Potential; Shapley value
Content Focus:Academic Audience
Peer Reviewed:Yes
Rankings:AJG Ranking / 3
SJR Ranking / Q1
Licence (German):License LogoUrheberrechtlich geschützt