3} A fun, game-loving professor wants to play a guessing game with Home and her 49 classmates. Each of the students simultaneously and privately writes down a number between zero and l on a piece of paper, and the professor will compute the mean of these numbers and call it 2. The student who submits the number closest to (EVE-PEI} wins $50 yes, the 9 is inside the parenthesis unlike what we saw in class. It'multiple students tie, they split the prize equally. a. Find a symmetric Nash equilibrium to this game. What number is a best response to everyone else submitting that same number? b. Show that choose the number 5 is a dominatedfnon-rationaliaable strategy. (Hint: what would the class average 2'. have to be for the target number to be 5?] c. Similarly. show that choosing the number 90 is a dominated strategy. d. What are all the dominated strategies? (Hint: think about your answers to b and c to help you with this}