CMA Final · Strategic Cost Management · Game Theory
Payoffs to Player A in a zero-sum game are: A1: 5 against B1 and 1 against B2; A2: 2 against B1 and 4 against B2. Which is the value of the game, using mixed strategies where required?
The value is 3. There is no saddle point because maximin is 2 and minimax is 4. Player A mixes A1 and A2 in the ratio 1:2, which makes A's expected payoff 3 whichever column B chooses.
- A2
- B3Correct
- C3.5
- D4
Explanation
Maximin = 2 and minimax = 4, so there is no saddle point. A plays A1 with probability (4-2)/[(5+4)-(1+2)] = 2/6 = 1/3. Value = (5x4 - 1x2)/6 = 18/6 = 3. Check: against B1, 5/3 + 2x2/3 = 3, and against B2, 1/3 + 4x2/3 = 3. Choosing 2 or 4 wrongly takes the maximin or minimax as the value.
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