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CMA Final · Strategic Cost Management · Game Theory

Two rival firms, A and B, choose strategies simultaneously. The table shows A's gain (₹ lakh); B's loss is the same amount. Rows are A's strategies A1, A2, A3; columns are B's strategies B1, B2, B3. A1: 2, 6, 4. A2: 5, 7, 6. A3: 3, 8, 1. What is the value of the game?

The game value is ₹5 lakh. A's best guaranteed row minimum is 5 (A2) and B's best column maximum is also 5 (B1). Since maximin equals minimax, a saddle point exists at A2 and B1, so the game is solved in pure strategies.

  1. A₹5 lakh, with a saddle point at (A2, B1)Correct
  2. B₹6 lakh, since A2 yields 6 against B3
  3. C₹7 lakh, the largest entry in A2's row
  4. DNo pure-strategy value, because no saddle point exists

Explanation

Row minima are 2, 5 and 1, so the maximin is 5 (A2). Column maxima are 5, 8 and 6, so the minimax is 5 (B1). Maximin equals minimax, so a saddle point exists at (A2, B1) and the value is 5. Saying there is no saddle point is wrong because the two values coincide.

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