Deck 11: Decision Theory

Question 1

Decision theory always guarantees optimal solution.

Answer 1

False

Question 2

Decision theory provides a rational and logical way of making decisions.

Answer 2

True

Question 3

All decision theory problems have two or more alternatives.

Answer 3

True

Question 4

The outcomes of a decision theory problem are usually known with certainty.

Question 5

States of nature are decision alternatives under the decision maker's control.

Question 6

Payoffs are exclusively associated with decision alternatives and are not related to the states of nature.

Question 7

Risk in the context of decision theory implies that the probabilities of the states of nature are known.

Question 8

In problems involving decision making under complete uncertainty, probabilities of states of nature are provided.

Question 9

In problems involving decision making under complete uncertainty, Hurwicz criterion with $\alpha=1.0$ will give the same answers as the maximin criterion.

Question 10

In problems involving decision making under complete uncertainty, Hurwicz criterion with $\alpha=1.0$ will give the same answers as the maximax criterion. True.

Question 11

Expected value of perfect information (EVPI) cannot be negative but may be 0 .

Question 12

Expected value of perfect information (EVPI) will be greater than expected opportunity loss associated with the EMV maximizing decision.

Question 13

Opportunity loss of a decision can never be negative.

Question 14

Expected value of perfect information is the lower bound of the money that may be spent to obtain perfect information that would resolve the uncertainty.

Question 15

Expected opportunity loss is the opportunity loss due to imperfect information.

Question 16

Expected opportunity loss is always less than expected value of perfect information in any problem.

Question 17

In a decision tree, a circle represents a decision node.

Question 18

In pruning (evaluating) a decision tree, you write the expected payoff at a random outcome node inside the circle or square representing that node.

Question 19

In pruning (evaluating) a decision tree, you place the largest of the payoff values coming out of a decision node inside the circle or square representing that node.

Question 20

Even if a decision problem involves a sequence of decisions in combination with various random events, payoff table approach can be used to solve the problem.

Question 21

Expected value of perfect information can be 0 for some problems.

Question 22

Expected value of sample information can be 0 for some problems.

Question 23

Expected profit under certainty is equal to the expected value of perfect information for all payoff tables.

Question 24

If expected profit under certainty is equal to the expected monetary value for a payoff table, then the expected value of perfect information must be 0 .

Question 25

Using sensitivity analysis, one can check whether the "best" decision continues to be the "best" decision over a wide range of probabilities.

Question 26

In solving decision theory problem with 2 random outcomes and three decisions the graphs use probability of one of the random outcomes in the X-axis and the other random outcome on the Yaxis.

Question 27

In solving decision theory problems with 2 random outcomes and 3 decisions, there will be at most 3 ranges on the probability of one of the random outcomes and a different optimal decision in each range.

Question 28

In solving a sensitivity analysis problem in a decision theory problem with 2 random outcomes and three decisions, the final result will depend on which random outcome's probability was plotted on the Xaxis.

Question 29

Using utility values of the decision maker, instead of monetary values, may change the "best" decision in a decision theory problem.

Question 30

One can solve a decision theory problem with utility values and present the "best" decision to those who want to use utility, instead of monetary values, and it will work for all users who want to use utility.

Question 31

Which of the following is not a part of decision tree problem specification?

A) A list of alternatives
B) A list of possible states of nature
C) Expected value of perfect information
D) Payoffs associated with alternative/state of nature combination

Question 32

If a decision theory problem has 3 decision alternatives and 4 states of nature, the number of payoffs in that problem will be

A) 3
B) 4
C) 12
D) 64

Question 33

In a decision theory problem under complete uncertainty, which one of the following approaches will not be possible?

A) Expected monetary value
B) Maximin
C) Minimax
D) Hurwicz

Question 34

Projected payoff corresponding to various levels of business expansion and economic conditions faced by Ramcast Cable Inc. is given in the table below. Using maximax criteria identify the correct decision for Ramcast Cable Inc.

A) $d_{1}$
B) $d_{2}$
C) $d_{3}$
D) $d_{4}$

Question 35

Projected payoff corresponding to various levels of business expansion and economic conditions faced by Ramcast Cable Inc. is given in the table below. Using maximin criterion, identify the correct decision for Ramcast Cable Inc.

A) $d_{1}$
B) $d_{2}$
C) $d_{3}$
D) $d_{4}$

Question 36

Projected payoff corresponding to various levels of business expansion and economic conditions faced by Ramcast Cable Inc. is given in the table below. Using minimax regret criterion, identify the correct decision for Ramcast Cable Inc.

A) $d_{1}$
B) $d_{2}$
C) $d_{3}$
D) $d_{4}$

Question 37

Projected payoff corresponding to various levels of business expansion and economic conditions faced by Ramcast Cable Inc. is given in the table below. Using Hurwicz criterion with $\alpha=0.7$ , identify the correct decision for Ramcast Cable Inc.

A) $d_{1}$
B) $d_{2}$
C) $d_{3}$
D) $d_{4}$

Question 38

Expected payoff corresponding to various levels of business expansion and economic conditions faced by Ramcast Cable Inc. is given in the table below. The probabilities of the events are also given. Using expected monetary value criterion, identify the correct decision for Ramcast Cable Inc.

A) $d_{1}$
B) $d_{2}$
C) $d_{3}$
D) $d_{4}$

Question 39

Expected payoff corresponding to various levels of business expansion and economic conditions faced by Ramcast Cable Inc. is given in the table below. The probabilities of the events are also given. What is the maximum expected monetary value (EMV) in the payoff matrix given below?

A) 210,000
B) 241,000
C) $-10,000$
D) $-15,000$

Question 40

Projected payoff corresponding to various levels of business expansion and economic conditions faced by Ramcast Cable Inc. is given in the table below. Using minimizing opportunity loss criterion, identify the correct decision for Ramcast Cable Inc.

A) $d_{1}$
B) $d_{2}$
C) $d_{3}$
D) $d_{4}$

Question 41

Expected payoff corresponding to various levels of business expansion and economic conditions faced by Ramcast Cable Inc. is given in the table below. The probabilities of the events are also given. What is the minimum expected opportunity loss in the payoff matrix given below?

A) 180,000
B) 435,000
C) 390,000
D) 149,000

Question 42

Projected payoff corresponding to various levels of business expansion and economic conditions faced by Ramcast Cable Inc. is given in the table below. What is the expected value if perfect information (EVPI) is given for the decision faced by Ramcast Cable Inc.?

A) 210,000
B) 241,000
C) 149,000
D) 390,000

Question 43

Projected payoff corresponding to various levels of business expansion and economic conditions faced by Ramcast Cable Inc. is given in the table below. What is the expected profit under certainty (EPC) for the decision faced by Ramcast Cable Inc.

A) 210,000
B) 241,000
C) 149,000
D) 390,000

Question 44

Expected payoff corresponding to various levels of business expansion for \href{http://ThingsJamaica.com}{ThingsJamaica.com} Inc. is given in the table below. The probabilities of the events are also given. What is the maximum expected monetary value (EMV) corresponding to the EMV maximizing decision?

A) 270,000
B) 250,000
C) 4,000
D) 485,000

Question 45

Expected payoff corresponding to various levels of business expansion for \href{http://ThingsJamaica.com}{ThingsJamaica.com} Inc. is given in the table below. The probabilities of the events are also given. What is the expected profit under certainty (EPC) for this problem?

A) 270,000
B) 380,000
C) 4,000
D) 485,000

Question 46

Expected payoff corresponding to various levels of business expansion for \href{http://ThingsJamaica.com}{ThingsJamaica.com} Inc. is given in the table below. The probabilities of the events are also given. What is the expected value of perfect information (EVPI)?

A) 270,000
B) 110,000
C) 380,000
D) 130,000

Question 47

Prior probabilities for economic boom, moderate growth, and recession in the Land of the Bipeds are given below. There is a Land of Mortals where there are only two states: Boost or Roast. Conditional probability of Boost or Roast, given various states of economic conditions in the Land of the bipeds, is also known and presented below.

The $\mathrm{P}($ Boost $)$ is

A) 0.16
B) 0.15
C) 0.46
D) 0.54

Question 48

Prior probabilities for economic boom, moderate growth, and recession in the Land of the Bipeds are given below. There is a Land of Mortals where there are only two states: Boost or Roast. Conditional probability of Boost or Roast, given various states of economic conditions in the Land of the bipeds, is also known and presented below.

The $\mathrm{P}($ Roast) is

A) 0.16
B) 0.54
C) 0.46
D) 0.04

Question 49

Prior probabilities for economic boom, moderate growth, and recession in the Land of the Bipeds are given below. There is a Land of Mortals where there are only two states: Boost or Roast. Conditional probability of Boost or Roast, given various states of economic conditions in the Land of the bipeds, is also known and presented below.

The $\mathrm{P}($ Boom/Boost $)$ is

A) 0.435
B) 0.348
C) 0.370
D) 0.296

Question 50

Prior probabilities for economic boom, moderate growth, and recession in the Land of the Bipeds are given below. There is a Land of Mortals where there are only two states: Boost or Roast. Conditional probability of Boost or Roast, given various states of economic conditions in the Land of the bipeds, is also known and presented below.

The $\mathrm{P}$ (Recession/Roast) is

A) 0.087
B) 0.761
C) 0.074
D) 0.648

Question 51

Prior probabilities for economic boom, moderate growth, and recession in the Land of the Bipeds are given below. There is a Land of Mortals where there are only two states: Boost or Roast. Conditional probability of Boost or Roast, given various states of economic conditions in the Land of the bipeds, is also known and presented below.

The $\mathrm{P}($ Recession/Roast) is

A) 0.087
B) 0.761
C) 0.074
D) 0.648

Question 52

Jim Smith is weighing all the pros and cons of his three job offers at the end of his MBA program. His expected salary and benefits are related to the economic conditions that may be experienced in the next 3 years, the planning horizon for his first post-MBA job. Jim hypothesizes that the economy may be in one of two states-high unemployment or low unemployment. The details of the dollar benefits during the next 3 years, under various conditions, are given below in the table.

What is range of probability of high unemployment that will make the stock analyst position EMV maximizing alternative?

A) $(0,0.3)$
B) $(0,0.5)$
C) $(0.4,1.0)$
D) $(0,0.625)$

Question 53

Jim Smith is weighing all the pros and cons of his three job offers at the end of his MBA. program. His expected salary and benefits are related to the economic conditions that may be experienced in the next 3 years, the planning horizon for his first post-MBA job. Jim hypothesizes that the economy may be in one of two states-high unemployment or low unemployment. The details of the dollar benefits during the next 3 years, under various conditions, are given below in the table.

What is range of probability of high unemployment that will make the stock analyst position EMV maximizing alternative?

A) $(0,0.3)$
B) $(0,0.5)$
C) $(0,0.4)$
D) $(0.4,1.0)$

Question 54

Jim Smith is weighing all the pros and cons of his three job offers at the end of his MBA program. His expected salary and benefits are related to the economic conditions that may be experienced in the next 3 years, the planning horizon for his first post-MBA job. Jim hypothesizes that the economy may be in one of two states-high unemployment or low unemployment. The details of the dollar benefits during the next 3 years, under various conditions, are given below in the table.

What is the range of probability of high unemployment that will make the Marketing Manager Trainee position EMV maximizing alternative?

A) $(0,0.4)$
B) $(0.4,0.5)$
C) $(0.4,1.0)$
D) $(0.5,1.0)$

Question 55

Jim Smith is weighing all the pros and cons of his three job offers at the end of his MBA program. His expected salary and benefits are related to the economic conditions that may be experienced in the next 3 years, the planning horizon for his first post-MBA job. Jim hypothesizes that the economy may be in one of two states-high unemployment or low unemployment. The details of the dollar benefits during the next 3 years, under various conditions, are given below in the table.

What is range of probability of high unemployment that will make the Service Manager Trainee position EMV maximizing alternative?

A) $(0,0.4)$
B) $(0.4,0.5)$
C) $(0.4,1.0)$
D) $(0.5,1.0)$

Question 56

In the following decision problem, you are considering two business opportunities at the end of your business education. One is a safe but less lucrative business (Bus-A) and the other a risky but attractive business (Bus-B). The expected five-year revenue differs significantly depending on boom, stagnation or recession in the national economy. The following table gives the payoff matrix and probabilities. At this time, you do not have reliable estimates of the probabilities of the economic conditions.

(A) What is the best decision using maximax criterion?
(B) What is the best decision using maximin criterion?
(C) What is the best decision using minimax regret criterion?
(D) What is the best decision using Hurwicz criterion with $\alpha=0.3$ ?

Question 57

In the following decision problem, you are considering two business opportunities at the end of your business education. One is a safe but less lucrative business (Bus-A) and the other a risky but attractive business (Bus-B). The expected five-year revenue differs significantly depending on boom, stagnation or recession in the national economy. The following table gives the payoff matrix and probabilities.

(A) Draw a decision tree.
(B) What is the best decision maximizing expected monetary value?
(C) What is the expected monetary value?
(D) What is the EVPI?
(E) What is the expected opportunity loss for each decision?
(F) What is the decision that minimizes expected opportunity loss?

Question 58

In the following decision problem, you are considering two business opportunities at the end of your business education. One is a safe but less lucrative business (Bus-A) and the other a risky but attractive business (Bus-B). The expected five-year revenue differs significantly depending on boom, stagnation or recession in the national economy. The following table gives the payoff matrix and probabilities.

(A) Suppose that you have an economist friend, who can look at a crystal ball and advise you. He predicts two states for the economy, namely "good" or "bad" for the economy during your planning horizon. The conditional probabilities of the state of economy and the random events related to your business are given below.
$\mathrm{P}($ good $/ \mathrm{s} 1)=0.7, \mathrm{P}(\operatorname{good} / \mathrm{s} 2)=0.35$ , and $\mathrm{P}(\operatorname{good} / \mathrm{s} 3)=0.1$
$\mathrm{P}(\mathrm{bad} / \mathrm{s} 1)=0.3, \mathrm{P}(\mathrm{bad} / \mathrm{s} 2)=0.65$ , and $\mathrm{P}(\mathrm{bad} / \mathrm{s} 3)=0.9$
Find the revised probabilities.
(B) Draw the decision tree and find the best decision, assuming that your friend will charge you $\$ 5000$ .
(C) What is EVSI?
(D) What is the efficiency of the sample information?

Question 59

Kathy Smith is contemplating her first major purchase of a lifetime, her own primary residence. Her planning horizon is 5 years, and she plans to sell the house in 5 years. She is wondering whether it will be a real estate boom or bust in the next 5 years. Her current probability estimate is 0.3 for boom and 0.7 for bust. The following table gives the net profit she expects to make for each combination of decision and random outcome.

(A) Find the EMV maximizing decision and the value of the best EMV.
(B) Using sensitivity analysis, find the range of probability for random outcome (Boom) and the corresponding EMV maximizing decision for each range.