5. (30%)

8 students are going on a trip on which they will live close together. Where

they are going, there is a disease which spreads easily among people who live close together.

There is a vaccination against the disease. The vaccination costs 3 for each student who gets

it. The students decide, individually and simultaneously, whether or not to get a vaccine. If

a student gets vaccinated, she will not get the disease and trip will brings her value 8. If she

is not vaccinated then the trip brings her value

m

, where

m

is the number of students who

get vaccinated. A student's payoff is the value of the trip minus the vaccination cost.

(a)

Is it a Nash equilibrium (NE) for everyone to get vaccinated? Explain your answer.

(5%)

(b)

Is it a NE for four people to get vaccinated? Explain your answer. (5%)

(c)

Is it a NE for five people to get vaccinated? Explain your answer. (5%)

(d)

Is it a NE for six people to get vaccinated? Explain your answer. (5%)

(e)

Find all the Nash equilibria in pure strategies. Explain your answer. (10%)