Problem #5: Cooperative Games (6 points): Suppose that there are 100 students individually
trying to decide between taking Game Theory or Public Economics. As we all know, it is harder
to get personalized help from the instructor in larger classes. Therefore, the more students in a
class, the less useful it is to any one of them. Let the payoffs and P from taking Game
Theory or Public Economics, respectively, be given by:
() = 500 −
P(P) = 556– 3P
A) Find all of the equilibria in this game (that involve whole numbers of students). (Hint: It
may help to restate the payoffs so that both are in terms of or both in terms of .)
B) Of the equilibria you found, which are stable, and which are unstable? For full credit,
your answer must be accompanied by a graph.
C) What allocation of students would maximize social welfare? Remember that there are
only 100 students.
