Question For the first six questions, consider Joe and Sally, two fourth-graders who have been caught in the school library breaking two major rules: chewing gum and reading c

For the first six questions, consider Joe and Sally, two fourth-graders who have been caught in the school library breaking two major rules: chewing gum and reading comic books when they are supposed to be reading a class assignment. Both offenses are punished in terms of days of after-school detention. In the case of gum, all students found chewing it are punished the same, regardless of who brought the gum to school, and it’s quite easy to find out who’s chewing it. In the case of comic books, however, the student(s) who supply comic books for others are punished much more harshly than the students who are simply reading them.

So the school principal, eager to look good at identifying and taking care of student problems due to a workplace evaluation coming up soon, pulls Joe and Sally aside separately. She tells each of them that if he/she will confess to bringing the comic books, he/she will receive a much smaller punishment (fewer days of detention). If both or neither confess, the number of days of detention will differ as described by the attached game in tree format. On that tree, C means to confess, and N means not to confess, while J and S are the first initials of each player. Everything else is the same as in the PowerPoints.

Using the information on the tree, which of the following is true? ( The tree is attached)

1.)
A. If only Joe confesses, Sally will receive 1 day of detention.
B. If only Sally confesses, Joe will receive 3 days of detention.
C. If both Joe and Sally confess, Sally will receive 3 days of detention.
D. If neither Joe nor Sally confesses, Joe will receive 6 days of detention.

2.
Continue working with the attached table portraying the game with Joe and Sally. Which of the following best describes Sally’s dominant strategy in this game?

A. confessing, but only if Joe does not confess
B. confessing, no matter what Joe does
C. not confessing, but only if Joe confesses
D. not confessing, no matter what Joe does

3.
Keep using the attached game in tree format concerning Joe and Sally.

The Nash equilibrium in this situation can be best described as

A. there is no Nash equilibrium
B. there is more than one Nash equilibrium
C. (Joe: confess, Sally: don’t confess)
D. (Joe: don’t confess, Sally: confess)
E. (Joe: confess, Sally: confess)
F. (Joe: don’t confess, Sally: don’t confess)

4.
Keep using the attached game in tree format concerning Joe and Sally.

Which of the following is true about this game’s Nash equilibrium?

A. It is stable.
B. It is not stable.
C. There is no Nash equilibrium.
D. None of the above.

5.
Keep using the attached game in tree format concerning Joe and Sally.

If you found a Nash equilibrium for the game, is there any choice Joe and Sally could agree to make that would make them both better off than the Nash equilibrium outcome? If so, what is it?

A. Yes; they could agree for one to confess and the other not to.
B. No; the Nash equilibrium is the best possible choice for both.
C. Yes; they could agree for both not to confess.
D. None of the above – there is no Nash equilibrium.

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