CMA Final · Strategic Cost Management · Game Theory
In a two-person zero-sum game, the payoffs to Player A (the maximiser) are: A1: 3, 5, 4 against B1, B2, B3; A2: 6, 7, 8; A3: 2, 9, 1. Player B is the minimiser. What is the value of the game?
The value of the game is 6. The maximin of the row minima (3, 6, 1) equals the minimax of the column maxima (6, 9, 8), so a saddle point exists at A2 and B1, and the game is solved with pure strategies.
- A5
- B6Correct
- C7
- D8
Explanation
Row minima are 3, 6 and 1, so maximin = 6. Column maxima are 6, 9 and 8, so minimax = 6. They are equal, so there is a saddle point at (A2, B1) and the value is 6. The value 8 is just the largest entry in A2's row and ignores B's minimising choice.
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