Consider the following 3-player static game with row player Batman (his choices are a and b), column player Catwoman (her choices are c and d), and matrix player Joker (his choices are left, middle and right): c c left d 1,1,5 1,0,1 b 0,0,0 0,1,0 middle d 1,1,3 1,0,0 b0,0,0 0,1,3 right c d 1,1,0 1,0,0 b 0,0,0 0,1,5 Il (a) Give a belief for Joker about his opponents' choice combinations that supports his choice of middle (i.e. such that middle is optimal for him). (7 marks) (b) Solve the game with iterated strict dominance. (8 marks) (c) Construct an epistemic model such that, for every choice found in (b) there exists a type such that: the choice is optimal for the type, and the type expresses common belief in rationality. . Consider the following 3-player static game with row player Batman (his choices are a and b), column player Catwoman (her choices are c and d), and matrix player Joker (his choices are left, middle and right): c c left d 1,1,5 1,0,1 b 0,0,0 0,1,0 middle d 1,1,3 1,0,0 b0,0,0 0,1,3 right c d 1,1,0 1,0,0 b 0,0,0 0,1,5 Il (a) Give a belief for Joker about his opponents' choice combinations that supports his choice of middle (i.e. such that middle is optimal for him). (7 marks) (b) Solve the game with iterated strict dominance. (8 marks) (c) Construct an epistemic model such that, for every choice found in (b) there exists a type such that: the choice is optimal for the type, and the type expresses common belief in rationality