Say that Townsville is deciding how many coal-fired energy plants to build to supply
its energy needs. Some people are more environmentally oriented and thus prefer fewer
plants, and some people think that the jobs and electricity that the plants provide are more
important. Hence people differ on how many plants they feel are necessary. An opinion
poll is taken asking each person how many plants she or he prefers. The results are that
14 percent of the population prefer 0 plants, 16 percent prefer 1 plant, 18 percent prefer 2
plants, 6 percent prefer 3 plants, 30 percent prefer 4 plants, and 16 percent prefer 5 plants.
a. Say that there are two candidates running for office, and the only relevant issue is how
many plants to build. Each candidate takes a position on how many plants to build, and
then each voter votes for the candidate which is closest to her own position or "ideal point."
For example, if candidate 1 is for 3 plants and candidate 2 is for 0 plants, a voter who prefers
2 plants will vote for candidate 1. If there is a "tie" (if two candidates are equally close to
a voter’s ideal point), then half of the votes go to each candidate. For example, if candidate
1 is for 2 plants and candidate 2 is for 0 plants, then half of the people who prefer 1 vote
for candidate 1 and half vote for candidate 2. Each candidate wants to maximize the total
number of votes she gets.
Model this as a strategic form game (the candidates move simultaneously) as in the Downsian
model. Find the pure strategy Nash equilibrium. Predict what positions the candidates will
take and how many plants the town will build.
b. Now say that there are three candidates. Is there a pure strategy Nash equilibrium which
is similar to what you found in part a.?
c. Now say that opinions shift. A new poll is taken, and it is found that 4 percent of the
population prefer 0 plants, 10 percent prefer 1 plant, 78 percent prefer 2 plants, 2 percent
prefer 3 plants, 2 percent prefer 4 plants, and 4 percent prefer 5 plants. Say there are two
candidates. Predict what positions the candidates will take and how many plants the town
will build.d. Now again say that there are three candidates. Is there a pure strategy Nash equilibrium
which is similar to what you found in part c.?
