Consider the following strategy prole. All students of all types announce they are type 12. Ben identies all students (regardless of their announcements) to be equally likely to be each type, and assigns them all grade 6. Regardless of whether or not this strategy prole is an equilibrium, what payos would result for each type of student and what average payos would result for Ben? Notice that, given the choices of the students, Ben is assigning grades optimally. Explain carefully whether or not this is an equilibrium.