A Teacher Curves the Final Exam Such That the Top

Multiple Choice

A teacher curves the final exam such that the top half of students get an A and the bottom half an F (so their grade depends only on relative and not absolute performance) . Suppose that there are equal numbers of two groups,the Brainiacs and the Numbskulls. If they both study or they both party,the Brainiacs will get the As but if the Brainiacs party and the Numbskulls study,the Numbskulls will get the As.Suppose further that they both dislike studying and both like good grades. Suppose all students of a type choose the same action (so we can view it as a two-player game) . The payoff matrix is ? Characterize the Nash equilibrium or equilibria:

A) There is only one equilibrium,in mixed strategies.
B) The Brainiacs study and the Numbskulls party.
C) There are two: in one,the Brainiacs study and the Numbskulls party,and in the other they do the reverse.
D) Both types party.