Please answer question 3 & 4

3. (15 points) Three students are enrolled in a class. At the end of the class, the professor announces that 1 point extra credit will be awarded to all students if at least two complete a course evaluation. The stu- dents decide whether or not to complete the evaluation independently and simultaneously. Evaluations are a hassle and cost each student 1 jolly to complete. Each student values the extra credit at 10 jollies. (a) Draw the strategic form of the game among the students. (b) Find all pure strategy Nash equilibria of this game. (c) Find one mixed strategy Nash equilibrium. 4. (15 points) Consider the same setup as the previous problem, except now the value of the extra credit to each student is their private infor- mation. In particular, if a student expects to get an A in the course 2 without the extra credit, the extra credit is worthless. If the student does not expect to get an A, the extra credit is worth 10 jollies. Each student believes that each student (including herself) expects to get an A with probability 30. These probabilities are independent. Each student's type is drawn by nature and revealed only to that student. Then the students simultaneously decide to complete an evaluation or not. An evaluation costs 1 jolly to complete. Find conditions on 39 such that it is a pure strategy Bayes Nash equilibrium for students complete the evaluation if and only if they do not expect to get an A