Consider a two player game in which player 1 can choose A or B. The game ends if he chooses A while it continues to player 2 if he chooses B. Player 2 can then choose C or D, with he game ending after C and continuing again with player 1 after D. Player 1 then can choose E or F, and the game ends after each of these choices. (a) Draw a game tree for this game. Is it a game of perfect or imperfect information? How many terminal nodes does the game have? How many information sets? (b) What are the pure strategy sets? (c) Suppose that the payoffs following choice A by player 1 are (2,0), following C by player 2 are (3,1), following E by player 1 are (0,0) and following F by player 1 are (1, 2). What are the Nash equilibria of this game? What are the subgame perfect Nash equilibria?
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