A5.docx - Assignment 5 Decision Theory and Games Q1 a The Excel QM spreadsheet Maximum of Hurwicz values is \$1600 thousands of dollars so Hurwicz

# A5.docx - Assignment 5 Decision Theory and Games Q1 a The...

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Assignment 5 Decision Theory and Games Q1: a) The Excel QM spreadsheet: Maximum of Hurwicz values is \$1600 thousands of dollars, so Hurwicz strategy is a1 = Sydney. b) The maximum of EMV is \$2000 thousands of dollars, so expected value strategy is a1 = Sydney. c) The minimum of expected regrets is \$200 thousands of dollars, so expected regret strategy is a1 = Sydney. d) Expected return WITH perfect information = ERPI = 0.4 * \$2500 thousands of dollars + 0.6*\$2000 thousands of dollars = \$2200 thousands of dollars Expected value OF perfect information = EVPI = \$2200 thousands of 1
dollars - \$2000 thousands of dollars = \$200 thousands of dollars. e) Type the data in the Excel QM spreadsheet: The probabilities given are: Pr(B1|s1) = 0.6; Pr(B1|s2) = 0.3; Pr(s1) = 0.4; Pr(B2|s1) = 0.4; Pr(B2|s2) = 0.7; Pr(s2) = 0.6. Pr(B1) = Pr(B1|s1)Pr(s1) + Pr(B1|s2)Pr(s2) = 0.6 * 0.4 + 0.3 * 0.6 = 0.42 Pr(B2) = Pr(B2|s1)Pr(s1) + Pr(B2|s2)Pr(s2) = 0.4 * 0.4 + 0.7 * 0.6 = 0.58 Pr(s1|B1) = Pr(B1|s1)Pr(s1) / Pr(B1) = 0.6 * 0.4 / 0.42 = 0.5714286 2
Pr(s2|B1) = Pr(B1|s2)Pr(s2) / Pr(B1) = 0.3 * 0.6 / 0.42 = 0.4285714 Pr(s1|B2) = Pr(B2|s1)Pr(s1) / Pr(B2) = 0.4 * 0.4 / 0.58 = 0.2758621 Pr(s2|B2) = Pr(B2|s2)Pr(s2) / Pr(B2) = 0.7 * 0.6 / 0.58 = 0.7241379 EV(a1|B1) = 2000, EV(a1|B2) = 2000; EV(a2|B1) = 1857.1429, EV(a2|B2) = 1413.7931; EV(B1) = 2000, EV(B2) = 2000.

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