1. 40 marks Dynamic Games Consider the following two-player dynamic game between Player 1 and Player 2. Player 1 moves at information sets 1.1 and 1.2. Player 2 moves at information set 2.1. At every outcome, the payoffs of Player 1 are listed first. (r)/B Answer the following questions. 1.2 1.1 (3, 10) C (s)/D E (1,9) (3,8) (4,7) (5,6) DE (a) 5 marks How many subgames does this game have? (b) 15 marks Find all subgame-perfect Nash equilibria (SPNEs) of this game. 20 marks For each SPNE from part (b), determine whether it is part of a weak sequential equilibrium (Perfect Bayesian equilibrium) of this game. [Hint: Start with the strategies from the SPNE and try to add appropriate beliefs. Do not forget to check sequential rationality and consistency of beliefs at all information sets where this is possible.]