CMA Final · Strategic Cost Management · Game Theory
A two-person zero-sum game has the following payoffs (in Rs lakh) to Player A, who chooses rows A1 to A3; Player B chooses columns B1 to B3. A1: 6, 3, 8. A2: 5, 2, 4. A3: 7, 1, 9. What is the value of the game for A?
The value is Rs 3 lakh. The largest row minimum (maximin) is 3 and the smallest column maximum (minimax) is also 3, so a saddle point exists at A1 and B2, and the game value equals that common figure.
- ARs 2 lakh
- BRs 3 lakhCorrect
- CRs 5 lakh
- DRs 7 lakh
Explanation
Row minima are 3, 2 and 1, so maximin is 3. Column maxima are 7, 3 and 9, so minimax is 3. They are equal, so there is a saddle point at (A1, B2) and the value is 3. Rs 2 lakh is the minimum of row A2, which is not the maximin.
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