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To solve the given \(2 \times 4\) zero-sum game graphically, we will follow these steps: ### Step 1: Understand the Payoff Matrix The payoff matrix for Player \(P_1\) is: \[ \begin{bmatrix} 1 & 3 & -3 & 7 \\ 2 & 5 & 4 & -6 \end{bmatrix} \] Here: - Rows represent Player \(P_1\)'s strategies. - Columns represent Player \(P_2\)'s strategies. ### Step 2: Identify Pure Strategies First, check for pure strategy solutions (saddle points): - Row Minimums: - Row 1: \(\min(1, 3, -3, 7) = -3\) - Row 2: \(\min(2, 5, 4, -6) = -6\) - Column Maximums: - Column 1: \(\max(1, 2) = 2\) - Column 2: \(\max(3, 5) = 5\) - Column 3: \(\max(-3, 4) = 4\) - Column 4: \(\max(7, -6) = 7\) There is no overlap between the row minimums and column maximums, so no ________ _____ ______ _____ ____ __________ _________ ___ _________ ______ __________.
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