### 8/19/2016 Unit 8 Homework Assignment (8.2) Ryan Manuel MAT230, section MAT230.31 MOD6 2016, Summer 2 2016 Instructor: Kathleen Ferguson WebAssign…

Please use attached file. Thank you

1. –/1 pointsBerrFinMath1 8.2.001.

For the game and mixed strategies, find the expected value.

Show My Work (Optional)

2. –/1 pointsBerrFinMath1 8.2.002.

For the game and mixed strategies, find the expected value.

Show My Work (Optional)

3. –/1 pointsBerrFinMath1 8.2.003.

For the game and mixed strategies, find the expected value.

Show My Work (Optional)

4. –/1 pointsBerrFinMath1 8.2.004.

For the game and mixed strategies, find the expected value.

Show My Work (Optional)

Unit 8 Homework Assignment (8.2) (Homework)

Let G = , r 2 −7 = and c =

4 5

12

12

1212

Let G = 2 −4 , r = and c =

−3 1

25

35

1545

Let G = 5 1 4 , r = and c =

−8 6 −3

12

12

1313

13

Let G = , r = 0 and c =

9 3

−5 7

−5 6

12

12

1545

8/19/2016 Unit 8 Homework Assignment (8.2)

https://www.webassign.net/web/Student/AssignmentResponses/

last?dep=13960005 2/4

5. –/6 pointsBerrFinMath1 8.2.005.

For the 2 × 2 game, find the optimal strategy for each player. Be sure to check for saddle points before using the formulas.

For row player R:

For column player C:

Find the value v of the game for row player R.

v =

Who is the game favorable to?

The game is favorable to the row player.

The game is favorable to the column player.

This is a fair game.

Show My Work (Optional)

6. –/6 pointsBerrFinMath1 8.2.006.

For the 2 × 2 game, find the optimal strategy for each player. Be sure to check for saddle points before using the formulas.

For row player R:

For column player C:

Find the value of the game for row player R.

v =

Who is the game favorable to?

The game is favorable to the row player.

The game is favorable to the column player.

This is a fair game.

Show My Work (Optional)

2 −5

1 2

r1 =

r2 =

c1 =

c2 =

7 1

−2 4

r1 =

r2 =

c1 =

c2 =

8/19/2016 Unit 8 Homework Assignment (8.2)

https://www.webassign.net/web/Student/AssignmentResponses/

last?dep=13960005 3/4

7. –/6 pointsBerrFinMath1 8.2.007.

For the 2 × 2 game, find the optimal strategy for each player. Be sure to check for saddle points before using the formulas.

For row player R:

For column player C:

Find the value of the game for row player R.

v =

Who is the game favorable to?

This game is favorable to the row player.

This game is favorable to the column player.

This is a fair game.

Show My Work (Optional)

8. –/11 pointsBerrFinMath1 8.2.008.

Represent the situation as a game and find the optimal strategy for each player. State your final answer in the terms of the original question.

Political scientists distinguish between two kinds of issues in elections campaigns: “positional” issues (voters have sharply divided and incompatible

views) and “valence” issues (voters agree on goals but are divided on the best ways to achieve them). In a race between the incumbent and the

challenger for state governor, a marketing survey found that if the incumbent focused on positional issues, she trailed the challenger by 5% if he

focused on the same kind of issues, but she led him by 5% if he concentrated on valence issues. If she focused on valence issues, she trailed him by

15% if he focused on the same kind of issues, but she led him by 25% if he concentrated on positional issues.

What does P represent?

P represents valence issues.

P represents positional issues.

What does V represent?

V represents positional issues.

V represents valence issues.

For the incumbent:

For the challenger:

In designing the incumbent’s TV ads for the campaign, what proportion should focus on positional issues?

%

Show My Work (Optional)

5 −9

−2 5

r1 =

r2 =

c1 =

c2 =

Challenger

P V

Incumbent P

V

% %

% %

r1 =

r2 =

c1 =

c2 =

8/19/2016 Unit 8 Homework Assignment (8.2)

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last?dep=13960005 4/4

9. –/15 pointsBerrFinMath1 8.2.010.

Represent the situation as a game and find the optimal strategy for each player. State your final answer in the terms of the original question.

In a section of Freshman Composition at your college, the English professor gives a daily quiz on either vocabulary or writing, and allows his students

to bring either a dictionary or a grammar textbook (but not both) to use during the quiz. Joe estimates that if he brings a dictionary, he can get a 100

on a vocabulary quiz but only an 80 on a paragraph revision, while with his grammar textbook, he can get a 90 on the revision but only a 70 on the

vocabulary quiz.

What does D represent?

D represents paragraph revision.

D represents vocabulary quiz.

D represents grammar textbook.

D represents dictionary.

What does G represent?

G represents vocabulary quiz.

G represents paragraph revision.

G represents grammar textbook.

G represents dictionary.

What does V represent?

V represents grammar textbook.

V represents paragraph revision.

V represents dictionary.

V represents vocabulary quiz.

What does P represent?

P represents paragraph revision.

P represents grammar textbook.

P represents vocabulary quiz.

P represents dictionary.

How should he decide each day what to bring?

He should ask his friend which book to bring.

He should always take the dictionary.

Flip a coin each day; take the dictionary if it is heads and the grammar textbook if it is tails.

He should always take the grammar textbook.

What grade can he be expected to earn?

Show My Work (Optional)

Quiz on

V P

Joe brings D

G

r1 =

r2 =

c1 =

c2 =

v =