CMA Final · Strategic Cost Management · Game Theory
Firm A's payoffs (₹ lakh) in a zero-sum game against Firm B are: A1 = (2, 4, 11) and A2 = (7, 4, 2), against B1, B2 and B3 respectively. A may use mixed strategies. What is the value of the game?
The value is ₹4 lakh. Whatever mix A uses, B can hold A to 4 by choosing B2, and A can guarantee 4 by playing A1 with a probability between 2/9 and 3/5. The B1-B3 intersection (5.21) ignores B2, and the pure maximin (2) understates what mixing achieves.
- A₹4.00 lakhCorrect
- B₹5.21 lakh
- C₹2.00 lakh
- D₹4.50 lakh
Explanation
Let A play A1 with probability p. Expected payoff is 7 - 5p against B1, 4 against B2 and 2 + 9p against B3. B picks the minimum of these. For 2/9 ≤ p ≤ 3/5 both the B1 and B3 payoffs are at least 4, so the minimum is 4. No p gives A more than 4, because B2 holds A to 4. The value is 4. The 5.21 option comes from intersecting only the B1 and B3 lines (p = 5/14) and ignoring B2. The 2 option is the pure maximin.
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