13

Consider the two-player, two-strategy, zero-sum game:

Y1 Y2

X1 2 1

X2 -2 4

Determine the Nash Equilibrium in this game.

a.

1

b.

2

c.

-2

d.

There is no Nash Equilibrium

e.

4

14

The Mathematics department of a large university is predicting the grades of its master's students for a particular course, MATH6200. Data was collected and students' test scores in this course are predicted by a multiple linear regression model. Dummy variables were used for Gender, and also to represent whether the student had a First Class, Second Class, or Pass degree in his/her Bachelor's studies.

The following are estimated coefficients of this model:

Estimate p-value

(Intercept) 3 0.018

Gender

(0 for Male, 1 for Female) 5 0.004

Study hours/week 1.25 0.005

Bachelor's First Class

(0 for No, 1 for Yes) 15 0.00001

Bachelor's Second Class

(0 for No, 1 for Yes) 10 0.00001

Student's age 0.3 0.0245

Celina is a 25-year old student, who obtained a First-Class Bachelor's degree. She studies for 50 hours each week. Using the model, determine Celina's score for MATH6200.

a.

79

b.

96

c.

82

d.

93

e.

87

15

There are three possibilities for a government to consider in the coming hurricane season: major storm, minor storm, or no storm. The probabilities of these occurrences are 0.1, 0.4, and 0.5 respectively. The government can prepare by either clearing rivers or securing property, but not both. It also has the option not to prepare.

From experience, the government has the following information available for decision-making:

If there is a major storm:

With cleared drains, the government can save $2m in damage.

With secured property, the government can save $1.5m in damage.

If there is a minor storm:

With cleared drains, the government can save $0.8m in damage.

With secured property, the government can save $0.5m in damage.

If there is no storm:

By clearing drains, the government will lose $0.3m in costs.

By securing property, the government will lose $0.2m in costs.

Calculate the Expected Value of Perfect Information.

a.

$0.25m

b.

$0.15m

c.

$0.50m

d.

$0m

e.

$0.52m

16

A real-estate developer has the choice to construct a new apartment complex. If the housing market is favourable, they will earn significant profits, but if it is not, they stand to lose significant amounts.

They believe that there is a 70% chance of a favourable market.

To aid their decision-making they can pay for a survey to give them better information on whether the housing market will be favourable or not.

There is a 65% chance that the survey will indicate a favourable market and a 35% chance that it will not.

The net profits for each branch, including all relevant revenues and costs are displayed to the rightmost end of the decision tree below. Other relevant probabilities are also included.

What is the expected monetary value (EMV) of this project?

a.

50,000 EMV < 55,000

b.

EMV 55000

c.

EMV < 40,000

d.

40,000 EMV < 45,000

e.

45,000 EMV < 50,000