QUESTION B3 [15 Marks] A decision maker faced with four decision alternatives an

Question

QUESTION B3 [15 Marks] A decision maker faced with four decision alternatives and four sates of nature develops the following profit payoff table. States of nature Decision alternative S_1 S_2 S_3 S_4 d_1 14 9 10 5 d_2 11 10 8 7 d_3 9 10 10 11 d_4 8 10 11 13 (a) State and use the average payoff strategy to choose the best decision. (3) (b) State and use the aggressive strategy to choose the best decision. (3) (c) State and use the conservative strategy to choose the best decision. (3) (d) State and use the opportunity loss strategy to make the best decision. (3) (e) Suppose the decision maker obtains information that enables the following probabilities assessments: P(s_1) = 0.5; P(s_2) = 0.2; P(s_3) = 0.2; and P(s_4) = 0.1. Use the expected value approach to determine the optimal strategy.

Explanation / Answer

Ans:

a)

Calculate the expected value for each decision alternative,d1 has the best or maximum expected value,so choose d1.

(14*0.5+9*0.2+10*0.2+5*0.1=7+1.8+2+0.5=11.3)

b)Optimistic or aggressive strategy(Best of best):

Maximum of maximum values pay-offs of respective atternatives is14,So,choose d1.

c)Conservative strategy

Maximum of the worst payoff is 9,so choose d3.

d)Minimax Regret approach(Opportunity loss approach)

First find out opportunity table,for each state choose maximum payoff,then subtract other entries in that column from this maximum value

Minimum of maximum regrets of respective alternatives is 5,so choose d3.

S1 S2 S3 S4 Expected value d1 14 9 10 5 11.3 d2 11 10 8 7 9.8 d3 9 10 10 11 9.6 d4 8 10 11 13 9.5

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