Strategies and Equilibrium: 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 the game ending after C and continuing again with player 1 after D. Player 1 can then choose E or F, and the game ends after each of these choices. a. Model this as an extensive-form game tree. Is it a game of perfect or imperfect information? b. How many terminal nodes does the game have? How many information sets? c. How many pure strategies does each player have? d. Imagine that the payoffs following choice A by player 1 are (2, 0), those following C by player 2 are (3, 1), those following E by player 1 are (0, 0), and those following F by player 1 are (1, 2). What are the Nash equilibria of this game? Does one strike you as more "appealing" than the other? If so, explain why.

12 Strategies and Equilibrium: 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 the game ending after C and continuing again with player 1 after D. Player 1 can then choose E or F, and the game ends after each of these choices. a. Model this as an extensive-fem game tree. Is it a game of perfect or imperfect information? b. How many terminal nodes does the game have? How many informa- tion sets? c. How many pure strategies does each player have? :1. Imagine that the payoffs following choice A by player i are {2, 0}. those following C by player 2 are {3, 1), those following E by player 1 are (0, D}. and those following F by player I are (l, 2). What are the Nash equilibria of this game? Does one strike you as more "appealing" than the other? If so, explain why