CMA Final · Strategic Cost Management · Game Theory
Player A's payoffs in a zero-sum game with no saddle point are: row A1 = 5 and 1; row A2 = 2 and 4 (columns B1 and B2). What probability should A assign to strategy A1 in the optimal mixed strategy?
A should play A1 with probability 1/3. Equating expected payoffs against B1 and B2 gives 2 + 3p = 4 - 3p, so p equals one third, which leaves two thirds for A2 and a game value of 3.
- A1/3Correct
- B1/2
- C2/3
- D3/5
Explanation
Equate A's expected payoff against both columns: 5p + 2(1-p) = 1p + 4(1-p), so 2 + 3p = 4 - 3p, giving p = 1/3. The game value is then 3. The figure 2/3 is the probability of A2, not A1.
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