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

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1 ieS u(i, S) = { w(S) i ¢S