Q1 (20 points) There are 213 students in ECOS3012. Each student must pick a real number r between 0 and 100 (including 0 and 100). Let y be equal to 2 x the average of everyone's number. A student's payoff is equal to 1 if his number r is equal to y, and 0 if it isn't. (a) Is there a Nash equilibrium in which all students pick the same number r = 50? Explain why it is or isn't a Nash equilibrium. (4 points) (b) Find all Nash equilibria of this game. Explain your answer. (8 points) (c) Let's now change the rule. Suppose that a student's payoff is equal to 1 if his number or is equal to y + 20, and 0 if it isn't. Find all Nash equilibria of this game. Explain your answer. (8 points)