Question 1

The risk premium is never negative for a conservative decision maker.

Accepted Answer

A) True 
 B)False

Question 2

Chez Paul is contemplating either opening another restaurant or expanding its existing location.The payoff table for these two decisions is: $$\begin{array} { l | c c c } 
& &{ \text { State of Nature } } \
\text { Decision } & s _ { 1 } & s _ { 2 } & s _ { 3 } \
\hline \text { New Restaurant } & - \$ 80,000 & \$ 20,000 & \$ 160,000 \
\text { Expand } & - \$ 40,000 & \$ 20,000 & \$ 100,000
\end{array}$$ Paul has calculated the indifference probability for the lottery having a payoff of $160,000 with probability p and F1F1F1S1F1F1F10$80,000 with probability (1F1F1F1S1F1F1F10p)as follows: $$\begin{array} { r c } 
\text { Amount } & \text { Indifference Probability } ( p ) \
\hline - \$ 40,000 & .4 \
\$ 20,000 & 7 \
\$ 100,000 & .9
\end{array}$$ 
a.Is Paul a risk avoider, a risk taker, or risk neutral?
b.Suppose Paul has defined the utility of F1F1F1S1F1F1F10$80,000 to be 0 and the utility of $160,000 to be 80. What would be the utility values for F1F1F1S1F1F1F10$40,000, $20,000, and $100,000 based on the indifference probabilities?
c.Suppose P(s1) = .4, P(s2) = .3, and P(s3) = .3. Which decision should Paul make? Compare with the decision using the expected value approach.

Accepted Answer

a.A risk avoider
b.

Question 3

Consider the following two-person zero-sum game.Assume the two players have the same three strategy options.The payoff table below shows the gains for Player A. $$\begin{array}{l}
\begin{array} { | c | c c c c | } 
&&\text { Player B }\
{ \text { Plaver } \mathrm { A } } & \text { Strategy } b _ { 1 } & \text { Strategy } b _ { 2 } & \text { Strategy } b _ { 3 } \
\hline \text { Strategy }a _ { 1 }  & 3 & 5 & - 2 \
\text { Strategy }a _ { 2 }  & - 2 & - 1 & 2 \
\text { Strategy } a _ { 3 } & 2 & 1 & - 5 \
\hline
\end{array}
\end{array}$$ Is there an optimal pure strategy for this game? If so,what is it? If not,can the mixed-strategy probabilities be found algebraically? What is the value of the game?

Accepted Answer

There is not an optimal pure strategy.
H

Question 4

Super Cola is considering the introduction of a new 8 oz.root beer.The probability that the root beer will be a success is believed to equal .6.The payoff table is as follows: $$\begin{array} { l | l c } 
& \text { Success } \left( s _ { 1 } \right) & \text { Failure } \left( s _ { 2 } \right) \
\hline \text { Produce } & \$ 250,000 & - \$ 300,000 \
\text { Do Not Produce } & - \$ 50,000 & - \$ 20,000
\end{array}$$ Company management has determined the following utility values: $$\begin{array} { l c c c c } 
\text { Amount } & \$ 250,000 & - \$ 20,000 & - \$ 50,000 & - \$ 300,000 \
\hline \text { Utility } & 100 & 60 & 55 & 0
\end{array}$$ 
a.Is the company a risk taker, risk averse, or risk neutral?
b.What is Super Cola's optimal decision?

Accepted Answer

a.Risk averse
b.Prod

Question 5

When and why should a utility approach be followed?

Accepted Answer

A utility approach should be followed wh

Question 6

The Dollar Department Store chain has the opportunity of acquiring either 3,5,or 10 leases from the bankrupt Granite Variety Store chain.Dollar estimates the profit potential of the leases depends on the state of the economy over the next five years.There are four possible states of the economy as modeled by Dollar Department Stores and its president estimates P(s1)= .4,P(s2)= .3,P(s3)= .1,and P(s4)= .2.The utility has also been estimated.Given the payoffs (in $1,000,000's)and utility values below,which decision should Dollar make? Payo ff Table$\quad\quad\quad\quad\quad\quad\text{State Of The Economy}\
\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\text{Over The Next 5 Years}$
$\begin{array}{l|rrrr}
Decision&s_{1} &s_{2} &s_{3} &s_{4} \
\hline
d_{1}--\text { buy } 10 \text { leases } & 10 & 5 & 0 & -20 \
d_{2}--\text { buy } 5 \text { leases } & 5 & 0 & -1 & -10 \
d_{3}--\text { buy 3 leases } & 2 & 1 & 0 & -1 \
d_{4}--\text { do not buy } & 0 & 0 & 0 & 0
\end{array}$ Utility Table $$\begin{array} { l r r r r r r r } 
\text { Payoff } ( \text { in } \$ 1,000,000 ' s ) & + 10 & + 5 & + 2 & 0 & - 1 & - 10 & - 20 \
\hline \text { Utility } & + 10 & + 5 & + 2 & 0 & - 1 & - 20 & - 50
\end{array}$$

Accepted Answer

Question 7

Consider the following problem with four states of nature,three decision alternatives,and the following payoff table (in $'s): $$\begin{array} { l | c c c c } 
& s _ { 1 } & s _ { 2 } & s _ { 3 } & s _ { 4 } \
\hline d _ { 1 } & 200 & 2600 & - 1400 & 200 \
d _ { 2 } & 0 & 200 & - 200 & 200 \
d _ { 3 } & - 200 & 400 & 0 & 200
\end{array}$$ The indifference probabilities for three individuals are: $$\begin{array} { r c c c } 
\text { Payoff } & \text { Person 1 } & \text { Person 2 } & \text { Person 3 } \
\hline
\$ 2600 & 1.00 & 1.00 & 1.00 \
\$ 400 & .40 & .45 & .55 \
\$ 200 & .35 & .40 & .50 \
\$ 0 & .30 & .35 & .45 \
- \$ 200 & .25 & .30 & .40 \
- \$ 1400 & 0 & 0 & 0
\end{array}$$ 
a. Classify each person as a risk avoider, risk taker, or risk neutral.
b. For the payoff of $400, what is the premium the risk avoider will pay to avoid risk? What is the premium the risk taker will pay to have the opportunity of the high payoff?
c. Suppose each state is equally likely. What are the optimal decisions for each of these three people?

Accepted Answer

a.Person 1 -- risk taker; Pers

Question 8

Consider the following two-person zero-sum game.Assume the two players have the same two strategy options.The payoff table shows the gains for Player A. $$\begin{array}{l}
\begin{array} { | c | c c c | } 
&&\text { Player B }\
\text { Plaver A } & \text { Strategy } b _ { 1 } && \text { Strategy } b _ { 2 } \
\hline \text { Strategy } a _ { 1 } & 3 && 9 \
\text { Strategy } a _ { 2 } & 6 && 2 \
\hline
\end{array}
\end{array}$$ Determine the optimal strategy for each player.What is the value of the game?

Accepted Answer

Mixed strategy:
Play

Question 9

The logic of game theory assumes that each player has different information.

Accepted Answer

A) True 
 B)False

Question 10

To select a strategy in a two-person,zero-sum game,Player A follows a ______ procedure and Player B follows a ______ procedure.

Accepted Answer

A) maximax, minimin 
B) maximax, minimax 
C) maximax, maximax 
D) maximin, minimax 
A) maximax, minimin 
B) maximax, minimax 
C) maximax, maximax 
D) maximin, minimax

Question 11

The purchase of insurance and lottery tickets shows that people make decisions based on

Accepted Answer

A) expected value. 
B) sample information. 
C) utility. 
D) maximum likelihood. 
A) expected value. 
B) sample information. 
C) utility. 
D) maximum likelihood.

Question 12

The expected utility approach

Accepted Answer

A) does not require probabilities. 
B) leads to the same decision as the expected value approach. 
C) is most useful when excessively large or small payoffs are possible. 
D) requires a decision tree. 
A) does not require probabilities. 
B) leads to the same decision as the expected value approach. 
C) is most useful when excessively large or small payoffs are possible. 
D) requires a decision tree.

Question 13

The probability for which a decision maker cannot choose between a certain amount and a lottery based on that probability is

Accepted Answer

A) the indifference probability. 
B) the lottery probability. 
C) the uncertain probability. 
D) the utility probability. 
A) the indifference probability. 
B) the lottery probability. 
C) the uncertain probability. 
D) the utility probability.

Question 14

The outcome with the highest payoff will also have the highest utility.

Accepted Answer

A) True 
 B)False

Question 15

Generally,the analyst must make pairwise comparisons of the decision strategies in an attempt to identify dominated strategies.

Accepted Answer

A) True 
 B)False

Question 16

A dominated strategy will never be selected by the player.

Accepted Answer

A) True 
 B)False

Question 17

Give two examples of situations where you have decided on a course of action that did not have the highest expected monetary value.

Accepted Answer

One example of a situation where I decid

Question 18

For the payoff table below,the decision maker will use P(s1)= .15,P(s2)= .5,and P(s3)= .35. $$\begin{array} { c | r c c } 
&& { \text { State of Nature } } \
\text { Decision } & { s _ { 1 } } & s _ { 2 } & s _ { 3 } \
\hline d _ { 1 } & - 5000 & 1000 & 10,000 \
d _ { 2 } & - 15,000 & - 2000 & 40,000
\end{array}$$ 
a.What alternative would be chosen according to expected value?
b.For a lottery having a payoff of 40,000 with probability p and F1F1F1S1F1F1F1015,000 with probability (1 F1F1F1S1F1F1F10 p), the decision maker expressed the following indifference probabilities. $$\begin{array} { r c } 
\text { Payoff } & \text { Probability } \
\hline 10,000 & .85 \
1000 & .60 \
- 2000 & .53 \
- 5000 & .50
\end{array}$$ Let U(40,000) = 10 and U(F1F1F1S1F1F1F1015,000) = 0 and find the utility value for each payoff. 
c.What alternative would be chosen according to expected utility?

Accepted Answer

a.EV(d₁)= 3250 and EV

Question 19

If the payoff from outcome A is twice the payoff from outcome B,then the ratio of these utilities will be

Accepted Answer

A) 2 to 1. 
B) less than 2 to 1. 
C) more than 2 to 1. 
D) unknown without further information. 
A) 2 to 1. 
B) less than 2 to 1. 
C) more than 2 to 1. 
D) unknown without further information.

Question 20

With a mixed strategy,the optimal solution for each player is to randomly select among two or more of the alternative strategies.

Accepted Answer

A) True 
 B)False

The risk premium is never negative for a conservative decision maker.

When and why should a utility approach be followed?

Consider the following two-person zero-sum game.Assume the two players have the same two strategy options.The payoff table shows the gains for Player A. Player B Plaver A Strategy Strategy Strategy 3 9 Strategy 6 2 Determine the optimal strategy for each player.What is the value of the game?

The logic of game theory assumes that each player has different information.

To select a strategy in a two-person,zero-sum game,Player A follows a procedure and Player B follows a procedure.

The purchase of insurance and lottery tickets shows that people make decisions based on

The expected utility approach

The probability for which a decision maker cannot choose between a certain amount and a lottery based on that probability is

The outcome with the highest payoff will also have the highest utility.

Generally,the analyst must make pairwise comparisons of the decision strategies in an attempt to identify dominated strategies.

A dominated strategy will never be selected by the player.

Give two examples of situations where you have decided on a course of action that did not have the highest expected monetary value.

If the payoff from outcome A is twice the payoff from outcome B,then the ratio of these utilities will be

With a mixed strategy,the optimal solution for each player is to randomly select among two or more of the alternative strategies.

Introduction

Introduction to Probability

Probability Distributions

Decision Analysis

Times Series Analysis and Forecasting

Introduction to Linear Programming

Linear Programming: Sensitivity Analysis and Interpretation of Solution

Linear Programming Applications in Marketing, Finance, and Operations Management

Distribution and Network Models

Integer Linear Programming

Advanced Optimization Applications

Project Scheduling: Pertcpm

Inventory Models

Waiting Line Models

Simulation

Markov Processes

Filters

Exam 5: Utility and Game Theory

The risk premium is never negative for a conservative decision maker.

When and why should a utility approach be followed?

Consider the following two-person zero-sum game.Assume the two players have the same two strategy options.The payoff table shows the gains for Player A. Player B Plaver A Strategy Strategy Strategy 3 9 Strategy 6 2 Determine the optimal strategy for each player.What is the value of the game?

The logic of game theory assumes that each player has different information.

To select a strategy in a two-person,zero-sum game,Player A follows a ______ procedure and Player B follows a ______ procedure.

The purchase of insurance and lottery tickets shows that people make decisions based on

The expected utility approach

The probability for which a decision maker cannot choose between a certain amount and a lottery based on that probability is

The outcome with the highest payoff will also have the highest utility.

Generally,the analyst must make pairwise comparisons of the decision strategies in an attempt to identify dominated strategies.

A dominated strategy will never be selected by the player.

Give two examples of situations where you have decided on a course of action that did not have the highest expected monetary value.

If the payoff from outcome A is twice the payoff from outcome B,then the ratio of these utilities will be

With a mixed strategy,the optimal solution for each player is to randomly select among two or more of the alternative strategies.

Introduction

Introduction to Probability

Probability Distributions

Decision Analysis

Times Series Analysis and Forecasting

Introduction to Linear Programming

Linear Programming: Sensitivity Analysis and Interpretation of Solution

Linear Programming Applications in Marketing, Finance, and Operations Management

Distribution and Network Models

Integer Linear Programming

Advanced Optimization Applications

Project Scheduling: Pertcpm

Inventory Models

Waiting Line Models

Simulation

Markov Processes

Filters

To select a strategy in a two-person,zero-sum game,Player A follows a procedure and Player B follows a procedure.