André Casajus, Frank Huettner

• We suggest a foundation of the Shapley value via 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, where the naïve solution assigns to any player the difference between the worth of the grand coalition and its worth after this player left the game.