Let (N, w) be a 0 1 normalized TP coalitional game, and let A be the set of all nontrivial coalitions A S N w(S) 0 Consider the following two player zero sum game Player 1 chooses a player i N and player 2 chooses a coalition S A The payoff (from 2 to 1) is Let Icirc acute be the value of the two person zero sum game Show that x core (N, w) Icirc acute yen 1 1 ieS u(i, S) w(S) i S

Question: Let (N, w) be a 0-1 normalized TP-coalitional game, and let A be the set of all nontrivial coalitions A = {S N : w(S)

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

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

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