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 10% if he focused on the same kind of issues, but she led him by 10% if he concentrated on valence issues. If she focused on valence issues, she trailed him by 25% if he focused on the same kind of issues, but she led him by 35% 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?