Suppose an amusement park is being built in a city with a
population of 100. Voluntary contributions are being solicited to cover the
cost. Each citizen is being asked to give $100. The more people contribute, the
larger the park will be and the greater the benefit to each citizen. But it is
not possible to keep out the noncontributors; they get their share of this
benefit anyway. Suppose that when there are n contributors in the population,
where n can be any whole number between 0 and 100, the benefit to each citizen
in monetary unit equivalents is n2 dollars.
(a) Suppose that initially no one is contributing. You
are the mayor of the city. You would like everyone to contribute and can use
persuasion on some people. What is the minimum number whom you need to persuade
before everyone else will join in voluntarily?
(b) Find the Nash equilibria of the game where each
citizen is deciding whether to contribute.