2. There are 91. students in E00316. Since they think Alex gives wonderful lectures, they are all attending a lecture one day and, at one point, all believe that she has made a mistake. Each student must simultaneously and independently decide whether to bring this to Alex's attention; she will address the potential mistake if at least one of the 71 students does so. A student obtains a payoff of v if Alex addresses the potential mistake, but any student who speaks up incurs a personal cost. With probability p, the students have correctly identied that Alex has made a mistake; any student who speaks up thus incurs a low personal cost cL. 1 But with probability (1 p), the perceived mistake is not in fact a mistake; any student who speaks up thus incurs a high personal cost CH. If no one speaks up, all students receive a payoff of zero. Assume v > CL and v > CH. (a) Find a symmetric Nash Equilibrium of this game. (b) How does the probability of a student speaking up change as the probability the students are correct increases? As the high personal cost increases