1.Represent the following strategic situation as an extensive-form game. Janet is a contestant on a popular game show, and her task is to guess behind which door Liz, another contestant, is standing. With Janet out of the room, Liz chooses a door behind which to standeither door A or door B. The host, Monty, observes this choice. Janet, not having observed Liz's choice, then enters the room. Monty says to Janet either "Red" or "Green" (which sounds silly, of course, but it is a silly game show). After hearing Monty's statement, Janet picks a door (she says either "A" or "B"). If she picks the correct door, then she wins $100. If she picks the wrong door, then she wins nothing. Liz wins $100 if Janet picks the wrong door and nothing if she picks the correct door. (Thus, Liz would like to hide from Janet, and Janet would like to find Liz.) Monty likes the letter A. If Janet selects door A, then this selection makes Monty happy to the tune of 10 units of utility. If she selects door B, then Monty receives 0 utility units.

Part a. Represent the game in extensive form

Part b: Is this a game of perfect information? Justify your answer.

Part c: Is this a game of perfect recall? Justify your answer.

Part d: For each player (Liz, Monty, and Janet), define his/her corresponding strategy space.

Remember: the strategy space of a player defines the set of all strategies available to the player in

the extensive form game.