Question

3 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 (for Students,Professor) are as follows Stud. show up to 1st class, Prof. threatens quiz, Stud. show up to 2nd class, Prof. gives quiz Stud. show up to 1st class, Prof. threatens quiz, Stud. show up to 2nd class, Prof. does not give quiz Stud. show up to 1st class, Prof. threatens quiz, Stud. don't show up to 2nd class, Prof. gives quiz Stud. show up to 1st class, Prof. threatens quiz, Stud. don't show up to 2nd class, Prof. does not give quiz Stud. show up to 1st class, Prof. does not threaten quiz, Stud. show up to 2nd class, Prof. gives quiz Stud. show up to 1st class, Prof. does not threaten quiz, Stud. show up to 2nd class, Prof. does not give quiz Stud. show up to 1st class, Prof. does not threaten quiz, Stud. don't show up to 2nd class, Prof. gives quiz Stud. show up to 1st class, Prof. does not threaten quiz, Stud. don't show up to 2nd class, Prof. does not give quiz Stud. don't show up to 1st class, Prof. threatens quiz, Stud. show up to 2nd class, Prof. gives quiz Stud. don't show up to 1st class, Prof. threatens quiz, Stud. show up to 2nd class, Prof. does not give quiz Stud. don't show up to 1st class, Prof. threatens quiz, Stud. don't show up to 2nd class, Prof. gives quiz Stud. don't show up to 1st class, Prof. threatens quiz, Stud. don't show up to 2nd class, Prof. does not give quiz Stud. don't show up to 1st class, Prof. does not threaten quiz, Stud. show up to 2nd class, Prof. gives quiz Stud. don't show up to 1st class, Prof. does not threaten quiz, Stud. show up to 2nd class, Prof. does not give quiz Stud. don't show up to 1st class, Prof. does not threaten quiz, Stud. don't show up to 2nd class, Prof. gives quiz Stud. don't show up to 1st class, Prof. does not threaten quiz, Stud. don't show up to 2nd class, Prof. does not give quiz 2,3 2,3 2,1 1,0 4,1 2,1 3.2 1,0 4,2 3.1 Please draw the game tree for this game. 3.2 How many subgames does this game have? 3.3 What is the subgame perfect Nash Equilibrium for this game? 3.4 Do students believe Professor's threat of a quiz?

Answer 1

S1: student attends 1st class

NS1: student doesn't attend 1st class

T; teacher threats

NT; doesn't threat

S2: student attends 2nd class

NS2: doesn't attend 2nd class

Q professor gives quiz

NQ: prof. Doesn't give quiz

31) S1. NSI NT S2 N8 8 /N 12 (213)

B) total subgames shown by red brackets on each singleton node

So total 15 subgames

c) now solving backwards

3.3) SPNE→ Solving Game backwands La13) g) (2i3) (33) (3,2) (4) (312) (112) (313) (412) 12(33) A) (41) (3192) SP NE Si Show un host dass NS2not Show u 2nd cla

D) students don't believe the threat bcoz it's off the Eqm path, hence it's not the credible threat, since professor threat of quiz doesn't constitute the SPNE, so it's not rational for professor to quiz , so students don't believe