Question

Question 2

A decision maker faced with four decision alternatives and four states 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 Marks)

(b) State and use the aggresive strategy to choose the best decision. (3 Marks)

(c) State and use the conservative strategy to choose the best decision. (3 Marks)

(d) State and use the opportunity loss strategy to make the best decision. (5 Marks)

(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. (6 Marks)

Answer 1

Solution from the given deta we have States of Nature Decision Alternative Sal 2 S_ 5 -3 a d-2 d_3 d_u payott @ Average payat strategy. . In average payott strategy averages of all the possile is calculated for each decision and the decision having highest cuesage payott & selected- Average of Laplace dal 14+9+10+5. - 3 -9.5 U dza 11+10+8+7 36 59 dada = 9+10+10 +11. d_4 = 8+10 +11+3 40 - 10 4 = 10.5 decision will & Hence by average payott strategy best be day with average payent of to: 5 The best decision is d_y . By Aggresive strategy.(es) manimum Shallgy ir In aggreswe Strategy a person is optimisht cand tend to select- a decision which has highest man payett (manimado)

dal 214 d_2= _3=1 4.4 = 13 - Hence best decision is di - Conserrative Strategy or mau min) - m Conservatie Shatryy a person s pessimistic and tend to select a decision which has highest min. payett (marimin). dl=5 da=7 d-329 d_u=8 . Hence best decision is d_3 6.- opportunity Loss Strategy or miniman in Regret (opportunity Loss) for decision under particular state of nature are the difference of best of under that state of nature and the Payott of the respective decision under that state of nature. - Areeage opportunity toss or a decision is the average it the segret 4 all the autcases for a particula decision In opportunity less strategy we select a decision having minimum average regret. 31 S2 S3 S4 d-2 3o 36 by 6 0 0 0

du - 8 do 6 0-3 = 5 d_4 = 6 . Hence best decision is d.3 Given that P(SI) -0.5 P(52)=0.2 , PS3)0.2 , PS4= This is simika to average payett strategy, the only difference is that now the expected payett is calculated as sum product of Probabilities and respective payotts for each decision Calculating Expected value for each decision alternative Expected value at di dis S. (P(S)) + S₂ (P (S₂))+53 (P(S3)) + Su (P(sy)) = 14(0-5) +0.209) +0.2 (10) +0.1(5) = 13 - Gpected blue at de d-z = 11(0.5) + 102062) 48 (0.2)+7 (6) 9.8 - Expected value at d-3 d3 9 (0.5)+ 10 (0.2) + 10(0:2) + (0-1) S = 9.6 - Expected value at dry du = 8(0.5) +10(0.2) + 11(012) + 13(0.1) d49.55 A Hence, The highest expected payoff is for dal - with expected paugott of 1163 * please rate *