1. Imagine a second grade class with 20 students in which each student has a best friend. For any pair of students 3: and y, if x is y's best friend, then y is is best friend. Suppose that the teacher realizes that there is no chalk in the classroom. She decides to send a student to the supply room to get some chalk. The teacher randomly chooses a student. That student must go to the supply room and must choose another student and offer that student the opportunity to accompany him to get the chalk. The second student may either accept or reject the rst student's offer to go to get the chalk. If the second student accepts the offer, both students go to get the chalk together. If the second student rejects the offer, then the rst stu dent goes to get the chalk alone. Each student ranks outcomes as follows: (a) Describe a player's strategy in this game. (The teacher is not con sidered a player, but rather takes the role of nature). (b) Describe the set of Nash equilibria of this game. (c) Describe the set of Subgame Perfect Nash equilibira of this game. ((1) [optional] Now suppose that we change the game so that we don't talk about best friends any more, but instead we say that x likes y the best. However, it is not necessarily true that if X likes y the best, then y likes it the best. The preferences are now