Question 1: Sequential Game Imagine the same Professor and Students are playing a sequential game. Students move first and decide to show up to class or to not show up. Professor moves second and decides whether to threaten a quiz for the next lecture or not. Students then decide whether to attend the next lecture or not. Professor, who has a quiz prepared, observes whether students attend or not and then decides finally whether or not to actually give the quiz. Payouts (where the first number is for the student and the second is for the professor) are as follows: Stud. show up to class 1, Prof. threatens quiz, Stud. show up to class 2, Prof. gives quiz 2,3 Stud. show up to class 1, Prof. threatens quiz, Stud. show up to class 2, Prof. does not give quiz 34 Stud. show up to class 1, Prof. threatens quiz, Stud. don't show up to class 2, Prof. gives quiz 2.2 Stud. show up to class 1, Prof. threatens quiz, Stud. don't show up to class 2, Prof. does not give quiz 43 Stud. show up to class 1, Prof. does not threaten, Stud. show up to class 2, Prof. gives quiz 2.3 Stud. show up to class 1, Prof. does not threaten, Stud. show up to class 2, Prof. does not give quiz 34 Stud. show up to class 1, Prof. does not threaten, Stud. don't show up to class 2, Prof. gives quiz 2.2 Stud. show up to class 1, Prof. does not threaten, Stud. don't show up to class 2, Prof. does not give quiz 44 Stud. don't show up to class 1, Prof. threatens quiz, Stud. show up to class 2, Prof. gives quiz 32 Stud. don't show up to class 1, Prof. threatens quiz, Stud. show up to class 2, Prof. does not give quiz 43 Stud. don't show up to class 1, Prof. threatens quiz, Stud. don't show up to class 2, Prof. gives quiz 2:1 Stud. don't show up to class 1, Prof. threatens quiz, Stud. don't show up to class 2, Prof. does not give quiz 5,2 Stud. don't show up to class 1, Prof. does not threaten, Stud. show up to class 2, Prof. gives quiz 3,2 Stud. don't show up to class 1, Prof. does not threaten, Stud. show up to class 2, Prof. does not give quiz 4,3 Stud. don't show up to class 1, Prof. does not threaten, Stud. don't show up to class 2, Prof. gives quiz 2,1 Stud. don't show up to class 1, Prof. does not threaten, Stud. don't show up to class 2, Prof. does not give quiz 5,3 (a) Draw the game tree for this game. (b) How many subgames does this game have? (c) What is the subgame perfect Nash Equilibrium for this game? (d) Do Students believe Professor's threat of a quiz