Question 2 {25 marks) Consider the following 3-player static game with me player Batman {his choices are a and b}, column player Colman (her choices are c and d), and matrix player Inim- {his choices are ig', middle and right): Iq middle right 6 d c d c d :3 1,1,5 :1 :1 1,1,0 1,0,0 0 0,0,0 0 0,1,3 0 0,0,0 0,1,5 | (a) Give a belief for joker about his opponents' choice combinations that supports his choice of middle (Le. such that middle is optimal for him}. (3" marks} (1)] Solve the game with iterated strict dominance. (8 marks} {1:} Construct an epistemic model such that, for ever):r choice found in {13} there exists a type such that: I the choice is optimal for the type, I and the type expresses common belief in rationality