Let (N, w) be a 0-1 normalized TP-coalitional game, and let G be the corresponding two-person zero-sum game described in the previous exercise with value δ. Show that δ ‰¥ 1 if (N, w) is balanced.
Previous exercise
Let (N, w) be a 0-1 normalized TP-coalitional game, and let A be the set of all nontrivial coalitions A = {S Š† N : w(S) > 0}. Consider the following two-player zero-sum game. Player 1 chooses a player i ˆˆ N and player 2 chooses a coalition S ˆˆ A. The payoff (from 2 to 1) is

Let δ be the value of the two-person zero-sum game. Show that
x ˆˆ core (N, w) ‡” δ ‰¥ 1

1 ieS u(i, S) = { w(S) i S