Deck 6: Decision Making Under Uncertainty

Question 1

In making decisions,we choose the decision with the largest expected monetary value at each node.

Answer 1

True

Question 2

In decision trees,a probability node (a circle)is a time when the decision maker makes a decision.

Answer 2

False

Question 3

The expected monetary value represents a long-run average.

Answer 3

True

Question 4

The expected monetary value (EMV)criterion is sometimes referred to as "playing the averages".

Question 5

The Excel add-in,PrecisionTree,enables you to draw and label a decision tree.

Question 6

In decision trees,a decision node (a square)is a time when the result of an uncertain event becomes known.

Question 7

Bayes' rule can be used for updating the probability of an uncertain outcome after observing the results of a test or study.

Question 8

EMV criteria guarantee good outcomes.

Question 9

A risk profile lists the full probability distribution.

Question 10

Expected monetary value is the weighted sum of the possible monetary outcomes.

Question 11

In general,the expected monetary values (EMV)represent possible payoffs.

Question 12

In a multistage decision problem,decisions and outcomes alternate.That is,a decision maker makes a decision,then some uncertainty is resolved,then the decision maker makes a second decision,then some further uncertainty is resolved,and so on.

Question 13

A strategy region graph is useful for seeing whether the decision changes over the range of the input variable.

Question 14

The Excel add-in,PrecisionTree,does not perform the folding-back procedure automatically.You will need to do that manually in order to perform sensitivity analysis on key input parameters.

Question 15

Tornado graphs and spider graphs can be used to determine which input variables have the most impact on the expected value in a decision problem.

Question 16

In decision trees,any branches leading into a node (from the left)have already occurred.

Question 17

In a single-stage decision problem,a single decision is made first,and then all uncertainty is resolved.

Question 18

A risk profile is a chart that represents the probability distribution of monetary outcomes for any decisions.

Question 19

Decision trees are composed of nodes (circles,squares,and triangles)and branches (lines).

Question 20

In decision trees,an end node (a triangle)indicates that the problem is completed; that is,all decisions have been made,all uncertainty has been resolved,and all payoffs/costs have been incurred.

Question 21

The certainty equivalent is the certain dollar amount a risk-averse decision maker would accept in order to avoid a gamble altogether.

Question 22

Rational decision makers are never willing to violate the expected monetary value (EMV)maximization criterion when large amounts of money are at stake.

Question 23

Prior probabilities are sometimes called likelihoods,the probabilities that are influenced by information about the outcome of an earlier uncertainty.

Question 24

The expected value of perfect information (EVPI)is the difference between the EMV with perfect information and the EMV with no additional information.

Question 25

In decision trees,probabilities are listed on probability branches.These probabilities are _____ events that have already been observed.

A)marginal due to
B)conditional on
C)averaged with
D)increased by

Question 26

Bayes' is useful in determining the value of perfect information (EVPI).

Question 27

EMV criterion provides a rational way of making decisions

A)under all circumstances.
B)when there is one outcome.
C)at least when the monetary payoffs and costs are of "moderate" size relative to the decision maker's wealth.
D)at least when the monetary payoffs and costs are large relative to the decision maker's wealth.
E)under none of these situations.

Question 28

The expected value of sample information (EVSI)is the difference between the EMV we can obtain with sample information and the EMV we can obtain without information.

Question 29

In decision trees,EMVs are calculated through a _____ process.

A)"pay it forward"
B)"going forward"
C)"folding back"
D)"historical evaluation"

Question 30

In decision trees,monetary values _____ the end nodes.

A)are shown in
B)are shown to the right of
C)appear above
D)are shown to the left of

Question 31

In a single-stage decision tree problem,you make _____ first and then all you wait to see a(n)_____.

A)decisions; uncertainty outcome
B)calculations; known outcome
C)EMV calculations; certain events
D)likelihoods; uncertain outcome

Question 32

The expected value of perfect information (EVPI)is the most the decision maker would be willing to pay for the sample information.

Question 33

Utility function is a function that encodes a person's or company's feelings toward risk.

Question 34

In decision trees,time proceeds from

A)left to right.
B)bottom to top.
C)top to bottom.
D)right to left.

Question 35

Expected monetary value (EMV)is

A)the average or expected value of the decision if you knew what would happen ahead of time.
B)the weighted average of possible monetary values,weighted by their probabilities.
C)the average or expected value of the information if it was completely accurate.
D)the amount that you would lose by not picking the best alternative.
E)a decision criterion that places an equal amount on all states of nature.

Question 36

The preferred criterion in decision making is

A)maximin.
B)maximax.
C)expected monetary value.
D)none of these choices.

Question 37

The expected value of perfect information (EVPI)is irrelevant concept since perfect information is almost never available at any price.

Question 38

There are three types of nodes that are used with the decision trees.They are the

A)mean nodes,variance nodes,and the standard deviation nodes.
B)probability nodes,risk nodes,and the expected value nodes.
C)supply nodes,demand nodes,and the expected value nodes.
D)decision nodes,probability nodes,and end nodes.

Question 39

The mean of a probability distribution is also called the

A)median.
B)standard deviation.
C)variance.
D)expected value.
E)normalized point.

Question 40

For a risk averse decision maker,the certainty equivalent is less than the expected monetary value (EMV).

Question 41

Construct a decision tree to identify the course of action that maximizes WTC's expected profit.Make sure to label all decision and chance nodes and include appropriate costs,payoffs and probabilities.

Question 42

A risk profile from PrecisionTree lists

A)the full probability distribution.
B)all possible outcomes and their corresponding utility.
C)all options and their possible outcomes.
D)the nodes and branches for each possible outcome.

Question 43

Generate a risk profile for each possible decision in this problem.Would this have any impact on your decision?

Question 44

Which sensitivity analysis chart is most useful for seeing how the optimal decision changes as selected inputs vary?

A)Strategy region chart
B)Tornado chart
C)Spider chart
D)All of these choices

Question 45

Mathematically,the utility function for risk adverse individuals is said to be _____ and/or _____.

A)decreasing,linear
B)decreasing,convex
C)increasing,linear
D)increasing,concave

Question 46

Utility functions are mathematical functions that transform monetary values - payoffs and costs - into _____ values.

A)expected
B)utility
C)EMV
D)anchor

Question 47

Construct a decision tree to identify the buyer's course of action that maximizes the expected profit earned by the chain from the purchase and subsequent sale of footballs in the coming year.

Question 48

The expected value of sample information (EVSI)is equal to

A)EMV with posterior information - EMV with prior information.
B)EMV with free perfect information - EMV free information.
C)EMV with perfect information - EMV without information.
D)EMV with free information - EMV without information.

Question 49

In the nomenclature of Bayes' Rule,which of the following are probabilities that are conditioned on information that is obtained?

A)Prior probabilities
B)Posterior probabilities
C)Marginal probabilities
D)Objective probabilities

Question 50

The solution procedure that was introduced in the book for decision trees is called the

A)folding-back procedure.
B)single-stage method.
C)risk profile method.
D)precision tree method.

Question 51

_____ can be used to determine which input variables have the most impact on the expected value in a decision problem.

A)Payoff tables
B)Risk profiles
C)Spider charts
D)Decision nodes

Question 52

Which of the following statements are true?

A)Sensitivity analysis is a process of seeing how optimal decision and EMV vary when one or more inputs vary.
B)Multistage decision problem is one where decisions and observations of uncertain outcomes alternate.
C)Contingency plan is a strategy in a multistage decision problem that specifies which decision to make for each possible outcome.
D)All of these choices are true.

Question 53

With regard to decision making,most individuals are _____.

A)risk averse
B)risk seekers
C)risk maximizers
D)EMV maximizers

Question 54

What is Bayes' Rule?

A)Bayes' Rule is a rule that provides a mathematical way of updating probabilities as new information becomes available.
B)Bayes' Rule is a rule that provides a mathematical way of calculating EMV.
C)Bayes' Rule is a rule that provides a mathematical way of calculating EVI.
D)None of these choices are correct.

Question 55

Generate a risk profile for each of WTC's possible decisions in this problem.Characterize the differences in risk for the different options.

Question 56

If x is a monetary value (a payoff if positive,a cost if negative),U(x)the utility of this value,and R > 0 is the risk tolerance,then the function U(x)= 1 - is called a(n)_____ utility.

A)Poisson
B)exponential
C)binomial
D)normal

Question 57

Exponential utility has an adjustable parameter called risk tolerance.The risk tolerance parameter measures

A)how much money the decision maker has to spend.
B)the decision maker's attitude toward risk.
C)how much risk there is in a given decision.
D)the probability of an unfavorable outcome.

Question 58

When the lines for two alternatives cross on a strategy region chart,this shows

A)a change in which decision alternative is optimal.
B)the point at which a decision was made.
C)the point where the rate of change in expected value is zero.
D)resolution of the uncertainty about the input variable.

Question 59

The expected value of perfect information (EVPI)is equal to

A)EMV with posterior information - EMV with prior information.
B)EMV with free perfect information - EMV with information.
C)EMV with free perfect information - EMV with no information.
D)EMV with perfect information - EMV with less than perfect information.

Question 60

PrecisionTree tornado and spider charts are

A)useful for seeing which inputs affect a selected EMV the most.
B)not useful for decision making processes.
C)useful for calculating EMVs.
D)all of these choices.

Question 61

Suppose that an actual (not perfectly reliable)credit report has the following characteristics based on historical data; in cases where the customer did not default on the approved loan,the probability of receiving a favorable recommendation on the basis of the credit investigation was 80%,while in cases where the customer defaulted on the approved loan,the probability of receiving a favorable recommendation on the basis of the credit investigation was 25%.Given this information,what are the posterior probabilities that an earthquake will and will not occur,given the geologists predictions?

Question 62

Because the core test can only sample a small part of the mine,Southport's geologists believe it is somewhat unrealistic to view it as a perfectly reliable test.Based on similar tests they have conducted in the past,they believe that if the metallurgical properties of the ore are actually High Grade,then the probability that this test will return "favorable" results is 0.95.If the metallurgical properties are Low Grade,the probability that this test will return "favorable" results is only 0.25.Otherwise,the test results will be considered "unfavorable".Given this information,what are the posterior probabilities that the ore will be a High Grade and Low Grade,given the core test report?

Question 63

What are the expected payoffs for the three alternatives?

Question 64

Show that this decision maker is indifferent between gaining nothing and entering a risky situation with a gain of $80,000 (probability 1/3)and a loss of $10,000 (probability 2/3).

Question 65

Should the credit union purchase the report if it costs $150?

Question 66

Suppose that an actual (not perfectly reliable)market research report has the following characteristics based on historical data: if the program is actually going to be a hit,there is a 90% chance that the market researchers will predict the program to be a hit,and if the program is actually going to be a flop,there is a 20% chance that the market researchers will predict the program to be a hit.Given this information,what are the posterior probabilities that a show will be a hit or a flop,given the market research report?

Question 67

The bank can thoroughly investigate the customer's credit record and obtain a favorable or unfavorable recommendation.If the credit report is perfectly reliable,what is the most the credit union should be willing to pay for the report?

Question 68

Construct a decision tree to help Southport identify the strategy that maximizes its expected profit for this investment.Make sure to label all decision and chance nodes and include appropriate costs,payoffs and probabilities.

Question 69

The network can conduct market research to determine whether a program will be a hit or a flop.If the market research report is perfectly reliable,what is the most the network should be willing to pay for it?

Question 70

Should Southport conduct the imperfect core test if it costs $250,000?

Question 71

If there is a 10% chance that one of the decision maker's family heirlooms,valued at $5,000,will be stolen during the next year,what is the most that she would be willing to pay each year for an insurance policy that completely covers the potential loss of her cherished items?

Question 72

The decision maker now has $10,000 and two possible decisions.For Alternative 1,she loses $500 for certain (x=$9,500).For Alternative 2,she loses $0 (x=$10,000)with probability 0.9 and loses $5,000 (x=$5,000)with probability 0.10.Which alternative maximizes the expected utility of her net wealth?

Question 73

Construct a decision tree to help the television network identify the strategy that maximizes its expected profit in responding to a newly proposed television program.Make sure to label all decision and chance nodes and include appropriate costs,payoffs and probabilities.

Question 74

Suppose that Southport could consider another alternative - postponing the go/no-go decision on the new venture and drilling for a core sample of the ore to determine with complete certainty its metallurgical property.How much should Southport be willing to pay for the core sample?

Question 75

Should the network purchase the report if it costs $160,000?

Question 76

Construct a decision tree to help Ms.Rich decide whether or not to purchase insurance.Note that the tree should minimize Ms.Rich's annual expected total cost,including the possible insurance premium,deductible payment,and damage payment.In your tree,make sure to label all decision and chance nodes and include appropriate costs,payoffs and probabilities.

Question 77

The station is most uncertain about the average monthly revenue associated with the rock format and an A1 audience.Construct a strategy region chart for this input variable with a possible range from $85,000 to $200,000.Does the optimal decision to select the country format change at any point in this range?

Question 78

Construct a decision tree to help the station identify its optimal format.Make sure to label all decision and chance nodes and include appropriate costs,payoffs and probabilities.

Question 79

Construct a decision tree to help the credit union decide whether or not to make the loan.Make sure to label all decision and chance nodes and include appropriate costs,payoffs and probabilities.