IEOPER3 Quiz 1

Question 1

Set of concepts, principles, tools, and techniques that aid the decision maker in dealing with complex decisions under uncertainty

Answer 1

Decision Theory

Question 2

Components of a DT Problem

Answer 2

Decision Maker (who makes the decision?)
Alternative Courses of Action (Controllable Aspect of the problem)
States of Nature or Events (Not under the decision maker’s control)
Consequences / Payoffs

Question 3

A discrete DT problem can be represented using a __________________

Answer 3

Decision Tree/ Tree Diagram

Question 4

A __________ node precedes the set of possible actions that can be taken by the decision maker.

Answer 4

Square

Question 5

A __________ node precedes the set of events or states of nature that could be encountered after a decision is made.

Answer 5

Round

Question 6

Nodes are connected with ________

Answer 6

Branches

Question 7

A _________ node must follow with the alternatives, and every alternative is followed by a __________ node

Answer 7

Square; Round

Question 8

Every round node must follow with the __________, wherein each round node would have the ________ number of events.

Answer 8

Events; Same

Question 9

Each alternative and event would have a ________________.

Answer 9

Consequence/Payoff

Question 10

If no probabilities are assigned to the possible consequences, then the decision situation is called ________________

Answer 10

Decisions under Uncertainty

Question 11

If probabilities are assigned, then the situation is called _________________.

Answer 11

Decisions under Risk

Question 12

In a decision matrix, also known as ____________, the rows represent the number of ___________, and the columns represent the number of ___________.

Answer 12

Payoff Table; Alternatives; Events/ States of Nature

Question 13

Methods for Decision Under Uncertainty

Answer 13

Laplace Criterion
Maximin Criterion
Minimax Criterion
Savage Minimax Regret Criterion
Hurwicz Criterion

Question 14

In using the Laplace Criterion, we do not have sufficient reason to conclude that probabilities are different. Hence, we assume that _____________________________.

Answer 14

All events are equally likely to occur (1/n; n = number of alternatives)

Question 15

For the Laplace Criterion, select the ______ value for a max problem and select the _______ value for a min problem

Answer 15

Highest; Smallest

Question 16

In using Minimax/Maximin, _____________ is used for profit payoffs while __________ is used for cost payoffs

Answer 16

Maximin; Minimax

Question 17

True or False. When doing DT methodologies, the same answer is expected for all methods.

Answer 17

False (due to different tolerance of risk per method)

Question 18

If the given is a profit table but the question is asking to solve the problem using a minimax approach, what should be done?

Answer 18

Treat it as a savage minimax regret criterion

Get the opportunity loss table, then do minimax

Question 19

In the Hurwicz Criterion method, the alpha is multiplied by the _____________ view, whereas the (1-alpha) is multiplied by the ______________.

Answer 19

Optimistic View (highest profit or lowest cost)

Pessimistic View (lowest profit or highest cost)

Question 20

For the Maximin Criterion, assuming values are expressed as profits, the method is as follows:

Answer 20

1. Select the worst (lowest) value from each alternative (row perspective)
2. From there, select the best among the worst (highest possible value)

Question 21

For the Minimax Criterion, assuming values are expressed as costs, the method is as follows:

Answer 21

1. Select the worst (highest) value from each alternative (row perspective)
2. From there, select the best among the worst (lowest possible value)

Question 22

For the Savage Minimax Regret Criterion, assuming values are expressed as profits, the method is as follows:

Answer 22

1. Construct a regret table wherein:
   max value - current value (for each column)
2. Using the regret table, conduct the minimax approach (assume these are costs)

Question 23

For the Savage Minimax Regret Criterion, assuming values are expressed as costs, the method is as follows:

Answer 23

1. Construct a regret table wherein:
   current value - min value (for each column)
2. Using the regret table, conduct the minimax approach

Question 24

Methods for Decision Under Risk

Answer 24

Bayes’ Rule
Expected Value- Variance Criterion
Decision Making with Experimentation

Question 25

In using the Expected Value-Variance Criterion, if the values are expressed as profits, the formula is as follows:

Answer 25

Maximize E(z) - K var (z) wherein: var(z) = E(z^2) - [E(z)]^2

Question 26

In using the Expected Value-Variance Criterion, if the values are expressed as costs, the formula is as follows:

Answer 26

Minimize E(z) + K var (z) wherein: var(z) = E(z^2) - [E(z)]^2

Question 27

If ENGS > 0, then ___________

Answer 27

It is worthwhile to get additional information (proceed with posterior analysis)

Question 28

If ENGS < 0, then ___________

Answer 28

It is not worthwhile to get additional information

Question 29

ENGS

Answer 29

Expected net gain from sampling

Question 30

EPPI

Answer 30

Expected Profit from a perfect information source

Question 31

EVPI

Answer 31

Expected value of the perfect information source

Question 32

EP

Answer 32

Bayes' Expected Profit without experimentation

Question 33

Formula for EVPI

Answer 33

EVPI = EPPI - EP

Question 34

EVSI

Answer 34

Expected value of sample information

Question 35

CAI

Answer 35

Cost of getting additional information

Question 36

Formula for EVSI

Answer 36

EVSI = EPSI - EP

Question 37

Formula for ENGS

Answer 37

ENGS = EVSI - CAI

Question 38

Formula for EPPI

Answer 38

Payoff * (Probability); Get the best value for each state of nature/ event

Question 39

Formula for EP

Answer 39

Best result from the Bayes' Rule computation

Question 40

Formula for EPSI

Answer 40

Sum of all outcomes: E(P)*(Probability of Outcome n)

Question 41

____________________ considers the question of deciding whether or not it would be worthwhile to get additional information or to perform experimentation

Answer 41

Preposterior Analysis

Question 42

______________ deals with the optimal choice and evaluation of an action subsequent to all experimentation and testing using the experimental results

Answer 42

Posterior Analysis

Question 43

These are the initial possibilities without the benefit of experimentation

Answer 43

Prior Probabilities

Question 44

These refer to the revised probability values obtained after experimentation

Answer 44

Posterior Probabilities

Question 45

A decision maker using the criterion of realism might want to select an alpha value of 0.9 if he is:

Answer 45

Optimist

Question 46

A decision maker using the criterion of realism might want to select an alpha value of 0.1 if he is:

Answer 46

Pessimist

Question 47

In decision theory, it is assumed that: A. Any number of states of nature can occur altogether B. Only two states of nature can occur together C. Only one state of nature can occur at any time D. None of the above

Answer 47

C

Question 48

What is the difference between the Expected Profit of Posterior Information and the Expected Profit from Prior Information?

Answer 48

Expected Value of Sample Information (EVSI)

Question 49

Which among the following is not true of Utility Theory: A. Risk-averse people have decreasing marginal utility of money B. The Decision Maker is indifferent between two alternatives having the same utility values C. Consequences with utility value will produce the same results as those with monetary value D. Risk-seekers are people who have increasing marginal utility of money

Answer 49

C

Question 50

What is the difference between the expected profit under risk and the expected profit with perfect information is called:

Answer 50

Expected Value of Perfect Information (EVPI)

Question 51

The Laplace or criterion of rationality is also known as:

Answer 51

Principle of Insufficient Reason

Question 52

When the decision maker possesses information about the probabilities of the possible states of nature, his decisions may be made under conditions of:

Answer 52

Risk (Copilot)

Question 53

In a decision problem with five possible alternative decisions with seven states of nature, the payoff table will have:

Answer 53

35 payoffs

Question 54

The difference between the payoff of some particular decision and the state of nature, and the optimal decision for that state of nature is called:

Answer 54

Regret

Question 55

A generic term involving conflict situations of a particular sort

Answer 55

Game

Question 56

______________ refers to a set of tools and techniques for decisions under uncertainty involving two or more intelligent opponents in which each opponent aspires to optimize his own decision at the expense of the other opponents

Answer 56

Game Theory

Question 57

In game theory, an opponent is referred to as a __________.

Answer 57

Player

Question 58

The outcomes or payoffs of a game are summarized as functions of the different _________ for each player

Answer 58

Strategies

Question 59

Major Assumptions of Game Theory

Answer 59

1. Players - The number of players may be two or more 2. Timing - the conflicting parties decide simultaneously 3. Conflicting Goals - each party is interested in maximizing its own goal at the expense of the other 4. Repetition - most instances involve repetitive solutions 5. Payoff - payoffs for each combination of decisions are known by all parties 6. Information Availability - all parties are aware of all pertinent information

Question 60

Define Zero-Sum Games

Answer 60

The winner's earnings is equal to the loser's losses

Question 61

_______________ refers to a prescribed solution in which one alternative is repeatedly recommended to each player

Answer 61

Pure Strategy

Question 62

Branches that come out of a round node should always ___________

Answer 62

Be equal to 1

Question 63

Branches that come out of a square node do not need a _____________

Answer 63

Probability

Question 64

In a given game matrix, how is maximin and minimax obtained?

Answer 64

Maximin - Get the lowest value for each row player strategy then select the highest value (max of the minimums) Minimax - Get the highest value for each column player strategy then select the lowest value (minimum of the maximums)

Question 65

Define a Saddle Point

Answer 65

Lowest in the row, highest in the column Optimal solution for a pure strategy problem

Question 66

Methods that can be used to solve for optimal solution of pure strategy problem:

Answer 66

Maximin/ Minimax Principle of Dominance

Question 67

Rules of Domination for Principle of Dominance

Answer 67

Row: Dominating row should have entries LARGER than and / or equal to (with at least one entry larger than) to the entries in the dominated row Column: Dominating column should have entries SMALLER than and / or equal to (with at least one entry smaller than) to the entries in the dominated row Dominated rows/ columns can be deleted from the table

Question 68

Conditions for scale up:

Answer 68

The remaining matrix, after using principle of dominance, must be bigger than a 2x2 (2x3 or 3x2 or higher) The scaled up value should be equal to the most negative number in the matrix

Question 69

True or False. Value of the game can be different from row and column player perspective

Answer 69

False (has to be the same)

Question 70

If the mixed strategy problem is reduced to a 2x2 matrix, what method should be used? Enumerate Steps

Answer 70

Analytical Method 1. Define Row Player X as the proportion of time row player uses strategy i 2. Make Equations (look at columns going down) 3. Solve unkowns using system of linear equations 4. Compute for E(vn) = equation from number 3 with substituted unknowns (should be equal) 5. Repeat process for Column Player Y (equations are made by looking per row)

Question 71

If the mixed strategy problem is reduced to a matrix that is higher than a 2x2 matrix, what method should be used? Enumerate Steps

Answer 71

LP Method: (SCALE UP MATRIX IFF THERE IS A NEGATIVE NUMBER) 1. Construct an LP model for the Row player wherein: MIN Z = X1 + X2 + Xn; n = number of strategies used by the row player Constraints: (Look at the matrix from a column perspective) <= 1 2. Solve for unknowns (if not given) 3. Compute for v: v= 1/ (X1 + X2+Xn) or v = 1/Z 4. Compute for the x values wherein x1 = vX1 x2 = vX2 and so on 5. If a scale up was done, the final value for v should be v - T. 6. Repeat process for Column player MAX Yo = Y1 + Y2 +Yn; n= number of strategies used b column player Constraints: (Look at the matrix from a row perspective) >= 1

Question 72

Hurwicz Criterion Procedure

Answer 72

1. Get highest and lowest values for each alternative 2. Multiply alpha to optimistic value (highest profit value/ lowest cost) and (1-alpha) to its counterpart for each alternative 3. If profit, select the alternative with the highest computed value If cost, select the alternative with the lowest computed value

Question 73

In using Mixed Strategy LP Model Method, the models of the row player and column player must be ______________ to one another.

Answer 73

A Primal and Dual Model Relationship

Question 74

True or False. In sequential decision making, the payoffs column refers to the latest values, not the total payoff.

Answer 74

True

Question 75

In a game matrix, given Player 1 perspective, the rows represent the _______ from Player _____ and the columns represent the _______ from Player _____.

Answer 75

Gains; Player 1 Losses; Player 2

Question 76

In a given game matrix wherein Player 1 comprise the rows and Player 2 comprise the columns, if we want to formulate a zero sum game matrix in the perspective of Player 2, we should ____________ and _____________ the matrix.

Answer 76

Transpose and Negate

Question 77

Procedure for Decision Making with Experimentation

Answer 77

1. Make first decision tree ( state of nature -> outcomes) 2. Multiply the pure probabilities with conditional probabilities to get intersection Probabilities 3. Make second decision tree (outcomes -> states of nature) 4. Get posterior probabilities by the following formula: intersection probability / (summation of outcome) 5. Make third decision tree (substitute states off nature probabilities with the posterior probabilities) 6. Solve for the values under favourable and unfavourable outcomes 7. Solve for EPSI, EVSI, and ENGS

Question 78

True or False. Multiple optimal solutions is possible in a game matrix

Answer 78

True

Question 79

Every constraint of the row player is a ___________ to the column player.

Answer 79

Strategy

Question 80

A mixed strtaegy problem occurs if there is __________.

Answer 80

No saddle point