(Solution) - Let N w be a 0 1 normalized TP coalitional game and -(2025 Original AI-Free Solution)

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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 ?. Show that ? ? 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 ? 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