Question: 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),

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): left c d 1,1,5 1,0,1 b0,0,0 0,1,0 middle d 1,1,3 1,0,0 b 0,0,0 0,1,3 right d 11 1,1,0 1,0,0 0 0,0,0 0,1,5 11 (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. 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): left c d 1,1,5 1,0,1 b0,0,0 0,1,0 middle d 1,1,3 1,0,0 b 0,0,0 0,1,3 right d 11 1,1,0 1,0,0 0 0,0,0 0,1,5 11 (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

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