Consider the game played in class called "2/3 of the average" and our discussion of the way you played it. As you may remember, the unique Nash Equilibrium in this game is the action profile in which all the players play a strategy of zero. a) Show that any other action profile, different from (0, 0, ..., 0), is not a Nash Equilibrium. Be as formal as possible in your explanations. b) Why in this game played once it was unlikely to observe the players playing a Nash equilibrium strategy of zero? What is the role of beliefs in explaining this phenomenon? c) Is the action profile (0, 0, ..., 0) the dominant strategy equilibrium? If yes, please show that this is the case. If not, explain why.