3. Consider the centipede game described on slide 6 of the slide set \"Games of Perfect Information: Examples and Applications.\" a) How many pure strategies does each player have? b) Find the subgame-perfect equilibrium of this game. c) Find the subgame-perfect equilibrium outcome of this game. (1) Find a Nash equilibrium that is not subgame-perfect. e) (Harder) Show that every pure-strategy Nash equilibrium must lead to the subgame- perfect equilibrium outcome. [Hintz proceed by contradiction. That is, assume that there is a NE leading to a different outcome, and ShOW that one of the players would not be best responding, which contradicts the assumption]