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CMA Final · Strategic Cost Management · Game Theory

Two rival firms, A and B, play a zero-sum game. The matrix shows A's gain in ₹ lakh (B's loss) for each pair of strategies. A chooses rows A1 to A3 and B chooses columns B1 to B3. A1: 6, 2, 8 A2: 5, 4, 7 A3: 3, 1, 9 What is the value of the game to A?

The value is ₹4 lakh. A's best guaranteed row minimum is 4 (row A2) and B's lowest column maximum is also 4 (column B2). Because maximin equals minimax, a saddle point exists at A2 and B2, so both play pure strategies and the game value is 4.

  1. A₹4 lakhCorrect
  2. B₹2 lakh
  3. C₹5 lakh
  4. D₹6 lakh

Explanation

Row minima are 2, 4 and 1, so maximin = 4 (row A2). Column maxima are 6, 4 and 9, so minimax = 4 (column B2). Since maximin equals minimax, there is a saddle point at (A2, B2) and the value is 4. The figure 6 is only the largest column maximum, not the minimax.

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