1.The suave and sophisticated economics instructor announces to the class prior to the final exam that he will curve the grades so that the average grade on the exam will be B+.The unruly mob of a class gets together to conspire against the goodhearted educator.The class figures that if they all agree to hand in blank final exams that no one will have to study, and everyone will earn a grade of B+; this would yield a high level of utility to the slackers.Of course, one danger for the students is that some of the student may "cheat" and complete the exam, thereby improving their own grades at the expense of everyone else's; this would yield even higher utility to the "cheaters", and somewhat lower utility for the slackers.If left unchecked all students may actually end up studying (say it ain't so), completing the exam, yielding a class average of B+.This would lower the "cheaters" utility, but raise the slackers utility, relative to the point where some cheated and some didn't, but obviously it would lower everyone's utility relative to the point where no one studied and everyone "earned" a B+.

a.Develop a game theory matrix that indicates the utility rewards for students that hand in blank and completed exams, depending on what other students do. (5)

b.What is the Nash equilibrium in your matrix? (5)

c.How can the students minimize the risk anyone will actually complete their exam? (5)

d.If the professor gets wind of the collusive behavior, what measures can he take to increase the chances that students complete the exams without going back on his word to curve the final grades? (5)