1. (30 points) There are three players, who are about to walk into a room one after the other. There is a switch in the room, which can be in one of three positions: Up, Middle, or Down. The players know the switch is initially in the Down position (they know this in parts a,b, and c below). When a player walks into the room he can change the switch position or leave it unchanged. A player who changes the switch position can only change it by one position. That is, if the switch is in D, he can move it to M, if the switch is in M, he can move it to D or to U, and if the switch is in U he can move it to M. The game ends after the third player walks into the room and makes his decision. (a) (10 points) Suppose that each player sees what all the players before him did. Draw the game in extensive form, ignoring payoffs. How many information sets and strategies does each player have? Explain. (b) (10 points) Suppose that when each player enters the room he only sees the position of the switch. Draw the game in extensive form, ignoring payoffs. How many information sets and strategies does each player have? Explain.