Q: 10 students are going on a trip on which they will live closetogether. Where they are going, there is a disease which spreadseasily among people who live close together. There is a vaccinationagainst the disease. The vaccination costs 3 for each student whogets it. The students decide, individually and simultaneously,whether or not to get a vaccine. There are two types of students:the pro-vaccine type and the anti-vaccine type. For a pro-vaccinetype, if she gets vaccinated, she will not get the disease and thetrip brings her value 10. For a anti-vaccine type, if she getsvaccinated, she will not get the disease and the trip brings hervalue 9. If a student does not get vaccinated then the trip bringsher value m, where m is the number of students who get vaccinated.A student’s payoff is the value of the trip minus the vaccinationcost. Among the 10 students, 5 of them are pro-vaccine and 5 areanti-vaccine.

(a) Is there a NE in which some anti-vaccine types getvaccinated and some pro-vaccine types do not get vaccinated?Explain your answer. (5%)

(b) Is there a NE in which 5 students get vaccinated? Explainyour answer. (5%)

(c) Is there a NE in which 7 students get vaccinated? Explainyour answer. (5%)

(d) Find all the NE in pure strategies. Explain your answer. (10%)

{NE is Nash Equilibrium}