CMA Final · Strategic Cost Management · Game Theory
A's payoffs (₹ lakh) in a zero-sum game are, with rows A1, A2, A3 and columns B1, B2, B3: A1: 3, 6, 8. A2: 5, 4, 9. A3: 2, 3, 6. B wants to minimise A's payoff. After applying the dominance rule repeatedly, what is the value of the game?
The value is ₹4.5 lakh. B discards its third column and A discards its third row because both are dominated. In the remaining 2x2 game there is no saddle point, and equalising expected payoffs gives A1 probability one quarter and a value of 4.5.
- A4.5Correct
- B4.0
- C5.0
- D4.25
Explanation
B3 (8, 9, 6) is at least B1 (3, 5, 2) in every row, so B drops B3. Then A3 (2, 3) is dominated by A2 (5, 4), so A drops A3. The 2x2 game A1: 3, 6 and A2: 5, 4 has maximin 4 and minimax 5, so no saddle. 3p+5(1-p) = 6p+4(1-p) gives p = 1/4, and value = 5-0.5 = 4.5. Check: B's q = 1/2 gives 3(0.5)+6(0.5) = 4.5.
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