Question

5. Six students are going on a road trip in which they will live closely together. Where they are going, there is a disease which spreads easily among people who live close together. The value of the trip to a student who does not get the disease is 6. The value of the trip to a student who gets the disease is 0. There is a vaccination against the disease. The vaccination costs different amounts for different students (they have different health plans). Let's call the students 1, 2, 3, 4, 5 and 6 respectively. The vaccination costs 1 for student 1; it costs 2 for student 2; etc.... If a student gets vaccinated, she will not get the disease. But, if she is not vaccinated then her probability of getting the disease depends on the total number in the group who are not vaccinated. If she is the only person not to get vaccinated then the probability that she gets the disease is 1/6. If there is one other person who is not vaccinated (i.e., two in all including her) then the probability that she gets the disease is 2/6. If there are two other people who are not vaccinated (i.e., three including her) then the probability that she gets the disease is 3/6, etc.. The students decide individually and simultaneously whether to get the vaccination and their goal is to maximise their payoffs. a) Explain with reasons whether or not it is a Nash Equilibrium for students 1,2,3 and 4 to get vaccinated and students 5 and 6 not to get vaccinated. [3 points] b) Which students have strictly or weakly dominated strategies? [3 points]

Answer 1

answer of (A)​​​​​​answer of (B)