Question

6. Three strategies and three states of nature are given and payoffs represent profits. (i) What is the optimal strategy if we apply the criterion of pessimism? State of nature. Strategy N1 N2 N3 S1 47 49 43 S2 32 25 41 S3 51 30 14​

Answer 1

The optimal strategy using the criterion of pessimism (Maximin criterion) is identified by choosing the strategy with the highest minimum payoff, which is strategy S1, with a worst-case scenario payoff of 43.

Step-by-step explanation:

The concept in question pertains to decision-making under uncertainty, specifically using the criterion of pessimism, also known as the Maximin criterion. This criterion suggests choosing the strategy with the best worst-case scenario payoff.

In the provided payoff matrix, each strategy (S1, S2, and S3) corresponds to different profits (payoffs) for each state of nature (N1, N2, N3). To apply the criterion of pessimism:

• Identify the minimum payoff for each strategy: S1 has a minimum of 43, S2 has a minimum of 25, and S3 has a minimum of 14.
• Select the strategy with the highest of these minimum payoffs. Strategy S1, with the highest worst-case scenario payoff of 43, is the optimal strategy.

Without analyzing subjective probabilities for each state of nature, the criterion of pessimism focuses solely on mitigating risk by selecting the strategy that ensures the best possible outcome in the worst-case scenario.

It is particularly useful when decision-makers are conservative and want to avoid the most significant potential loss.