Deck 6: Decision Models

Question 1

The Bayesian approach in decision analysis:

A)utilizes sample information only.
B)utilizes prior information only.
C)chooses between sample and prior information.
D)combines sample and prior information.

Answer 1

D

Question 2

"Expected value" in decision analysis is synonymous with "most likely value."

Answer 2

False

Question 3

Theoretically, a payoff table is not limited to two dimensions.

Answer 3

False

Question 4

If it is assumed that each possible state of nature has an equal likelihood of occurrence, the expected value criterion will yield the same result as:

A)maximin.
B)minimax
C)maximax
D)the principle of insufficient reason.

Question 5

Which of the following criteria represents an aggressive/optimistic approach?

A)maximin
B)minimax
C)minimax regret
D)maximax

Question 6

In some cases, the Expected Value of Sample Information can exceed the Expected Value of Perfect Information.

Question 7

The indifference approach for assigning utility values asks the decision maker which of two alternatives is preferred: the payoff under consideration or a chance at the highest payoff with a risk of the lowest payoff.

Question 8

EVPI is the smallest expected regret of any decision alternative.

Question 9

The expected regret criterion will always yield the same optimal decision as which other criterion?

A)maximin
B)minimax
C)minimax regret
D)expected value

Question 10

The "principle of insufficient reason" indicates the decision maker's belief that any state of nature is as likely to occur as any other state.

Question 11

"Uncertainty" implies probabilities; "risk" implies ignorance.

Question 12

The difference between "risk" and "uncertainty" in decision analysis alludes to the difference between:

A)knowledge and uncertainty.
B)pessimism and optimism.
C)known and unknown probabilities.
D)aggression and conservatism.

Question 13

An aggressive decision maker would prefer the minimax regret criterion over the maximin criterion.

Question 14

The payoff table always has more states of nature than decision alternatives.

Question 15

The optimal decision can change merely by introducing an additional, non-optimal alternative when using the minimax regret criterion.

Question 16

The objective function in game theory is to maximize the value of the game.

Question 17

When using the maximax criterion, the optimal decision alternative may be determined by simple inspection of the payoff table.

Question 18

The states of nature in a payoff table should be mutually exclusive and collectively exhaustive.

Question 19

The expected value criterion ignores the decision maker's attitude toward risk.

Question 20

The Expected Value of Perfect Information is always a value greater than 0.

Question 21

Consider the payoff table in problem 16.Suppose that each state of nature is equally likely to occur and that two indicators, I1 and I2, are possible.The conditional probabilities for indicator I1 given the states of nature are as follows: P(I1|S1) = .1, P(I1|S2) = .2, P(I1|S3) = .3, and P(I1|S4) = .4.The expected value of sample information is:

A)0
B)5.50
C)45.50
D)90

Question 22

Consider the following payoff table in which D1 through D4 represent decisions, S1 through S4 represent states of nature, and the values in the cells represent profits. $\begin{array}{c}\begin{array}{c}\\ \text { D1 } &\\ \text {D2 } &\\ \text {D3} &\\ \text {D4} &\\\end{array}\begin{array}{|c|c|c|c|}\hline S 1 & S 2 & S 3 & S 4 \\\hline 30 & 20 & -50 & 100 \\\hline 60 & 120 & 40 & -80 \\\hline 20 & 0 & 60 & 80 \\\hline 40 & -60 & 80 & 80\\\hline\end{array}\end{array}$ Suppose that each state of nature is equally likely to occur.The expected value of perfect information is:

A)0
B)40
C)50
D)90

Question 23

Consider a decision making problem with three states of nature: S1, S2, and S3, for which P(S1) = .1 and P(S2) = .3.Suppose also that there are two possible sample indicators, I1 and I2, and the following conditional probabilities hold: P(I1|S1) = .2, P(I1|S2) = .4, and P(I1|S3) = .6.The P(S2|I2) is:

A).18
B).24
C).36
D).50

Question 24

Consider the decision analysis problem with states of nature S_i, decision alternatives A_j, and the following payoff table: $\begin{array}{llll}&\mathbf{S 1} & \text { S2 } & \text { S3 } & \text { S4 } \\A1&55 & 51 & 50 & 38 \\A2&39 & 42 & 42 & 48 \\A3&45 & 59 & 57 & 35\end{array}$ What is the preferred alternative when using the:
A.maximin criterion?
B.maximax criterion?
C.minimax regret criterion?
D.principle of insufficient reason?

Question 25

The fact that so many people enter sweepstakes and/or buy lottery tickets demonstrates the difference between:

A)the expected value and the expected utility criteria.
B)altruism and selfishness.
C)risk aversion and risk indifference.
D)certainty and uncertainty.

Question 26

Utilities are generally well approximated by monetary payoffs for:

A)risk-averse individuals.
B)risk-preferring individuals.
C)small businesses.
D)large corporations.

Question 27

Consider the payoff table in problem 7.The optimal decision under the maximin criterion is:

A)D1
B)D2
C)D3
D)D4

Question 28

Consider the following payoff table in which D1 through D4 represent decisions, S1 through S4 represent states of nature, and the values in the cells represent profits. $\begin{array}{c}\begin{array}{c}\\ \text { D1 } &\\ \text {D2 } &\\ \text {D3} &\\ \text {D4} &\\\end{array}\begin{array}{|c|c|c|c|}\hline \text { S1 } & \text { S2 } & \text { S3 } & \text { S4 } \\\hline-20 & 40 & 60 & 100 \\\hline 30 & 120 & 60 & -50 \\\hline 30 & 30 & 40 & 40 \\\hline 10 & -60 & 80 & 70 \\\hline\end{array}\end{array}$
The optimal decision under the maximax criterion is:

A)D1
B)D2
C)D3
D)D4

Question 29

In a two-person, zero-sum game, where you have two possible strategies, S1 and S2, solving the model yields the answer S1 = .60 and S2 = .40.What does this mean?

Question 30

Consider the payoff table in problem 7.Suppose that the probabilities of states of nature S2 and S3 occurring are equal and that the probability of state of nature S4 occurring is .50.If the probability of state of nature S1 occurring is three times the probability of state of nature S2 occurring, the optimal decision under the expected value criterion is:

A)D1
B)D2
C)D3
D)D4

Question 31

The decision maker who is neither optimistic nor pessimistic might use which criterion?

A)minimax
B)maximin
C)maximax
D)the principle of insufficient reason

Question 32

If costs/losses, rather than profits/gains, are concerned, the minimax criterion is equivalent to:

A)maximin.
B)maximax.
C)minimax regret.
D)minimin.

Question 33

Consider the payoff table in problem 7.The optimal decision under the principle of insufficient reason criterion is:

A)D1
B)D2
C)D3
D)D4

Question 34

Suppose in a decision analysis problem, the decision maker's decision is based only on the expected monetary value of the possible outcomes.What does this imply, concerning the decision maker's utility function? Explain.

Question 35

The maximin payoff criterion best serves what type of person?

A)Everyone.
B)Pessimistic or conservative.
C)Risk-neutral.
D)Risk-preferred.

Question 36

The expected value of perfect information (EVPI):

A)is the same as the expected return with perfect information (ERPI).
B)is never less than the expected value of sample information (EVSI).
C)does not require probabilities in its calculation.
D)requires the availability of sample information.

Question 37

What is the "principle of insufficient reason"?

Question 38

Using the table below, which plan has the greatest efficiency? $\begin{array}{rccc}&\text { Expected Return}& \text { Expected Return}&\text { Expected Return}\\&\text { With Sample }& \text { With Perfect }& \text { Using Expected }\\&\text { Information }& \text {Information }& \text {Value (EREV) }\\\text { I } & 15 & 20 & 10 \\\text { II } & 15 & 20 & 12 \\\text { III } & 18 & 25 & 10 \\\text {IV } & 16 & 20 & 10\end{array}$

A)I
B)II
C)III
D)IV

Question 39

Consider the payoff table in problem 7.The optimal decision under the minimax regret criterion is:

A)D1
B)D2
C)D3
D)D4

Question 40

What are the two steps to calculate regret values for states of nature?

Question 41

The world is not perfect, and we can never know the future with real certainty.Why, then, should we use the expected value of perfect information (EVPI)?

Question 42

Model the World Series as a decision tree.The Diamondbacks are playing the Yankees in a best of 7 series.That is, the series ends when one team wins 4 games.Assume each team has an equal chance to win each game.

Question 43

What is a "fair" game?

Question 44

What is the interpretation of the shadow price values in a Game Theory linear programming model sensitivity report?

Question 45

Define the three terms in the equation EVPI = ERPI - EREV.

Question 46

What is a "zero-sum" game? Give an example of a zero-sum game and an example of a game which is not zero-sum.