The Shapley value of TU games, differences of the cores of convex games, and the Steiner point of convex compact sets

We explore the implications of the possibility of decomposition of any TU game $v$ into the difference of two convex games $v_1$ and $v_2$, i.e. $v=v_1-v_2.$ In particular, we prove that the Shapley value of a game $v$ is the difference of the Steiner points of the cores $C(v_1)$ and $C(v_2),$ and, in particular, for a convex game $v$ the Shapley value is the Steiner point of its core. Some properties of this interpretation are studied. A new definition of the Weber set of a TU game is considered.