CMA Final · Strategic Cost Management · Game Theory
Firm A (maximiser) and firm B (minimiser) have the following payoff matrix, showing A's gain in ₹ crore. A1: 8, 5, 6 A2: 7, 9, 4 A3: 6, 4, 3 After eliminating all dominated strategies and solving the reduced game, what is the value of the game?
The value is ₹17/3 crore, about 5.67. Row A3 is dominated by A1 and column B1 is dominated by B3, leaving a 2x2 game of 5, 6 and 9, 4. It has no saddle point, so the mixed formula gives (20 − 54)/(−6) = 17/3.
- A₹5 crore
- B₹17/3 croreCorrect
- C₹6 crore
- D₹6.5 crore
Explanation
A3 is dominated by A1 (8>6, 5>4, 6>3), so it is removed. For B, column B3 (6, 4) is no worse than B1 (8, 7) in both rows, so B1 is removed. The reduced game is A1: 5, 6 and A2: 9, 4. It has no saddle point, since maximin = 5 and minimax = 6. Value = (5×4 − 6×9)/(5+4−6−9) = (−34)/(−6) = 17/3. The figures 5 and 6 are only the pure-strategy bounds.
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