In this article, we study cooperative games with limited cooperation possibilities, represented by a tree on the set of agents. Agents in the game can cooperate if they are connected in the tree. We first derive direct-sum decompositions of the space of TU-games on a fixed tree, and two new...

In this article, we provide a new basis for the kernel of the Shapley value (Shapley, 1953), which is used to construct a new axiom of invariance, and to provide a new axiomatic characterization of the Shapley value. This characterization only invokes marginalistic principles, and does not rely...