in a cooperative game with three players {A,B,C} and characteristic function given by v() = 0; v({A}) = v({B}) = v({C}) = 1, also v({A,B}) = 2; v({A,C}) = 3; v({B,C}) = 4; v(({A,B,C}) = 6.

Suppose that v(X) describes the profits that the set of agents X can earn if they cooperate with each other.

(a) What's the inequalities that characterize the core of the cooperative game

(b) Find the Shapley value payoff of each player in this cooperative game. Is the Shapley value of this game also a member of the core?