Bella Robinson and Steve Carson are running for a seat in the U.S. Senate. If both candidates campaign only in the major cities of the state, then Robinson is expected to get 80% of the votes; if both candidates campaign in only rural areas, then Robinson is expected get 75% of the votes; if Robinson campaigns exclusively in the city and Carson campaigns exclusively in the rural areas, then Robinson is expected to get 30% of the votes; finally, if Robinson campaigns exclusively in the rural areas and Carson campaigns exclusively in the city, then Robinson is expected to get 65% of the votes. (a) Construct the payoff matrix for the game. (Enter each percentage as a decimal.) Carson City Rural Robinson City Rural Is the game strictly determined? YesNo (b) Find the optimal strategy for both Robinson (row) and Carson (column). P = Q =
Bella Robinson and Steve Carson are running for a seat in the U.S. Senate. If both candidates campaign only in the major cities of the state, then Robinson is expected to get 80% of the votes; if both candidates campaign in only rural areas, then Robinson is expected get 75% of the votes; if Robinson campaigns exclusively in the city and Carson campaigns exclusively in the rural areas, then Robinson is expected to get 30% of the votes; finally, if Robinson campaigns exclusively in the rural areas and Carson campaigns exclusively in the city, then Robinson is expected to get 65% of the votes. (a) Construct the payoff matrix for the game. (Enter each percentage as a decimal.) Carson City Rural Robinson City Rural Is the game strictly determined? YesNo (b) Find the optimal strategy for both Robinson (row) and Carson (column). P = Q =
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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Bella Robinson and Steve Carson are running for a seat in the U.S. Senate. If both candidates campaign only in the major cities of the state, then Robinson is expected to get 80% of the votes; if both candidates campaign in only rural areas, then Robinson is expected get 75% of the votes; if Robinson campaigns exclusively in the city and Carson campaigns exclusively in the rural areas, then Robinson is expected to get 30% of the votes; finally, if Robinson campaigns exclusively in the rural areas and Carson campaigns exclusively in the city, then Robinson is expected to get 65% of the votes.
(a) Construct the payoff matrix for the game. (Enter each percentage as a decimal.)
Is the game strictly determined?
(b) Find the optimal strategy for both Robinson (row) and Carson (column).
| Carson | ||||||||||||||
| City Rural | ||||||||||||||
| Robinson | City Rural |
|
Is the game strictly determined?
YesNo
(b) Find the optimal strategy for both Robinson (row) and Carson (column).
| P | = |
|
| Q | = |
|
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