2. Consider the following extensive form game between 2 players (1, 2) and nature. 0 3 1 0 0 1 F N F 2 Q Strong Weak 0.9 Nature 0.1 B B 2 N N F 4 2 1 0 0 Initially nature determines whether player 1 is strong or weak. Then player 1 decides between consuming beer (B) or quiche (Q). Player 2, after observing 1's action, decides to be nice (N) or to fight (F). Answer the following questions, clearly justifying your answer. a) Are there Nash equilibria in which player 1 randomizes between B and Q for both of his types? b) Are there Nash equilibria in which player 1 randomizes between B and Q when strong, but not when weak? c) Are there Nash equilibria in which player 1 randomizes between B and Q when weak, but not when strong? d) Are there Nash equilibria in which player 1 chooses B when strong, Q when weak? e) Are there Nash equilibria in which player 1 chooses Q when strong, B when weak? 52. 5 N Q 1 B F 1