A company is considering three strategies S1 to S3. The expected profits (¥100 million) in a boom, normal and recession economy are 50, 30 and −10 for S1, 40, 25 and 5 for S2, and 30, 20 and 10 for S3, and the probabilities of each economy are unknown. Following the maximin principle (choose the strategy whose worst-case profit is largest), which strategy is chosen?

Answer: C. S3

The maximin principle compares the worst-case profit of each strategy. The worst cases are −10 for S1, 5 for S2 and 10 for S3 (¥100 million), so S3, whose worst case is largest, is chosen. The maximax principle, which chooses the strategy with the largest best-case profit, would choose S1, and the minimax regret principle, which chooses the strategy with the smallest maximum regret (the difference from the best strategy's profit in each economy), would choose S2 (maximum regrets: 20 for S1, 10 for S2 and 20 for S3). In decisions where probabilities are unknown, the strategy chosen depends on the principle used, and the maximin principle is a cautious approach that seeks to avoid losses.

• A. This is the strategy with the largest best-case profit (50), chosen under the maximax principle. In the worst case it makes a loss of 10.
• B. This is the strategy with the smallest maximum regret (10), chosen under the minimax regret principle.
• C. Correct. Its worst-case profit of 10 is the largest of the three strategies.