A new axiomatization of the Shapley-solidarity value for games with a coalition structure

In this paper, we propose a new kind of players as a compromise between the null player and the A-null player. It turns out that the axiom requiring this kind of players to get zero-payoff together with the well-known axioms of efficiency, additivity, coalitional symmetry, and intra-coalitional symmetry characterize the Shapley-solidarity value. This way, the difference between the Shapely-solidarity value and the Owen value is pinpointed to just one axiom.