CMA Final · Strategic Cost Management · Game Theory
In a two-person zero-sum game, the payoffs (in ₹ lakh) to Firm A are shown below. A chooses rows A1-A3 and B chooses columns B1-B3. Rows: A1 = (6, 8, 7); A2 = (4, 5, 9); A3 = (3, 2, 10). What is the value of the game to A?
The value is ₹6 lakh. The maximin of the row minima (6, 4, 2) equals the minimax of the column maxima (6, 8, 10), so a saddle point exists at A1-B1 and the game has a pure-strategy value of 6.
- A₹6 lakhCorrect
- B₹8 lakh
- C₹4 lakh
- D₹10 lakh
Explanation
Row minima are 6, 4 and 2, so maximin = 6. Column maxima are 6, 8 and 10, so minimax = 6. Maximin equals minimax, so there is a saddle point at (A1, B1) and the value is 6. The 8 option wrongly picks the largest entry in A's best row.
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