8.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 10% if he focused on the same kind of issues, but she led him by 20% if he concentrated on positional issues.

Challenger

P V

Incumbent P _____________% _______________%

V ______________% _______________%

What does P represent?

P represents positional issues.

P represents valence issues.

What does V represent?

V represents positional issues.

V represents valence issues.

For the incumbent:

r₁ =

r₂ =

For the challenger:

c₁ =

c₂ =

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

_________________%

9.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.

Quiz on

V P

Joe brings D___________ _________

G ___________ _________

What does D represent?

• D represents grammar textbook.
• D represents dictionary.
• D represents vocabulary quiz.
• D represents paragraph revision.

What does G represent?

• G represents paragraph revision.
• G represents grammar textbook.
• G represents vocabulary quiz.
• G represents dictionary.

What does V represent?

• V represents dictionary.
• V represents grammar textbook.
• V represents paragraph revision.
• V represents vocabulary quiz.

What does P represent?

• P represents dictionary.
• P represents grammar textbook.
• P represents paragraph revision.
• P represents vocabulary quiz.

r₁ =

r₂ =

c₁ =

c₂ =

v =

How should he decide each day what to bring?

• 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 dictionary.
• He should ask his friend which book to bring.
• He should always take the grammar textbook.

What grade can he be expected to earn?

=___________