Question

Problem 13-01 (Algorithmic) The following payoff table shows profit for a decision analysis problem with two decision alternatives and three states of nature: State of Nature Decision Alternative 210 130 75 130 280 75 a. Choose the correct decision tree for this problem 210 210 di S1 S1 280 280 130 130 S2 130 130 d2 d2 75 75 di S3 75 (iv) 130 210 S2 210 di S1 130 75 S2 130 210 210 S1 di $1 130 75 $2 S3 75 S3 280 S1 130 130 d2 S2 75 S1 S3 280 75 Model (iii) b. If the decision maker knows nothing about the probabilities of the three states of nature, what is the recommended decision using the optimistic, conservative, and minimax regret approaches? Model (iii) b. If the decision maker knows nothing about the probabilities of the three states of nature, what is the recommended decision using the optimistic, conservative, and minimax regret approaches? d2 di or d2 di Optimistic approach Conservative approach Minimax regret approach

Answer 1

Let's first identify the minimum payoff from each alternative:

D1: 75 coming from s3

D2: 75 coming from s3

From the minimax regret approach, we have to choose the alternative which has the highest minimum payoff. In this case, it is the same for both the alternatives. Hence, correct answer is d1 or d2.