A method for estimating the core of root game

It is showen that the base of grand (shadow) subcore coincides with the core of the root game in any TU-cooperative game. Comparing definitions of grand subcore and grand shadow subcore with description of aggregate-monotonic core leads to the formal geometrical coincidence of aggregate-monotonic core with either grand subcore or grand shadow subcore. The method for estimating the simplest set of equations and inequalities describing the core of a root game in TU-game with any number of players ($n\ge3$) is proposed. To develop the method dual theory and inductive method by B. Peleg are used.