Consider the following multi-stage game between Ann and Bob: Ann moves rst and can either choose "Right" (R) or "Down" (D). If she chooses D then the game ends and the payos are (1,0) (the rst number is the payo to Ann and the second to Bob). If she chooses R then it's Bob's turn and he can choose between r and d. If he chooses d then the game ends with payos (0,2), and if he chooses r then it's again Ann's turn to choose R or D. If she chooses D the game ends with payos (3,1), and if she chooses R then Bob moves one more time. He can either choose d and end the game with payos (2,4), or he can choose r and the game ends with payos (3,3).

(a) Draw the tree representation for this multi-stage game.

(b) Analyze this game using backward induction. What is the prediction of game theory regarding how this game would/should be played?

(c) If you were Ann, what would you choose in the rst node?