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Solutions Chapter 4

Solutions Chapter 4 - Solutions 4.1 No At least not if the...

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43 Solutions 4.1. No. At least, not if the decision tree and influence diagram each represent the same problem (identical details and definitions). Decision trees and influence diagrams are called “isomorphic,” meaning that they are equivalent representations. The solution to any given problem should not depend on the representation. Thus, as long as the decision tree and the influence diagram represent the same problem, their solutions should be the same. 4.2. There are many ways to express the idea of stochastic dominance. Any acceptable answer must capture the notion that a stochastically dominant alternative is a better gamble. In Chapter 4 we have discussed first-order stochastic dominance; a dominant alternative in this sense is a lottery or gamble that can be viewed as another (dominated) alternative with extra value included in some circumstances. 4.3. A variety of reasonable answers exist. For example, it could be argued that the least Liedtke should accept is \$4.63 billion, the expected value of his “Counteroffer \$5 billion” alternative. However, this amount depends on the fact that the counteroffer is for \$5 billion, not some other amount. Hence, another reasonable answer is \$4.56 billion, the expected value of going to court. If Liedtke is risk-averse, though, he might want to settle for less than \$4.56 billion. If he is very risk-averse, he might accept Texaco’s \$2 billion counteroffer instead of taking the risk of going to court and coming away with nothing. The least that a risk-averse Liedtke would accept would be his certainty equivalent (see Chapter 13), the sure amount that is equivalent, in his mind, to the risky situation of making the best counteroffer he could come up with. What would such a certainty equivalent be? See the epilogue to the chapter to find out the final settlement. The following problems (4.4 – 4.9) are somewhat trivial to solve in PrecisionTree. All that is necessary is for the student to draw the model. The instructor may want the students to do some of these problems by hand to reinforce the methodology of calculating expected value or creating a risk profile. 4.4. The Excel file “Problem 4.4.xls” contains this decision tree. The results of the run Decision Analysis button (fourth button from the left on the Precis ionTree toolbar) are shown in the worksheets labeled Statistics, RiskProfile, CumulativeRiskProfile, and ScatterProfile. The Professional Version of PrecisionTree will also generate a Policy Suggestion Report. The Policy Suggestion Report shows what option was chosen at each node. This report is not created by the student version. EMV(A) = 0.1(20) + 0.2(10) + 0.6(0) + 0.1(-10) = 3.0 EMV(B) = 0.7(5) + 0.3(-1) = 3.2 4.5. The Excel file “Problem 4.5.xls” contains this influence diagram. The most challenging part of implementing the influence diagram is to enter the payoff values. The payoff values reference the outcome values listed in the value table. The value table is a standard Excel spreadsheet with values of influencing nodes.

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Solutions Chapter 4 - Solutions 4.1 No At least not if the...

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