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(a) When A=1, B=0; C=6 and D=3
Left Middle Right
Henry Up (1,0) (6,2) (3,1)
Middle (2,4) (8,7) (5,5)
Down (1,2) (4,1) (6,3)
The pure strategy Nash equilibria when the values of A,B,C,D are as above, are (middle,middle) and (down, right). For finding the mixed strategy Nash equilibrium, we have to see whether there is a dominated strategy for the players. For Henry, Up is dominated by Middle and for Dorothy, Left is dominated by Right. As dominated strategies are not used by the players in an equilibrium, Henry would randomize between Middle and Down and Dorothy would randomize between Middle and Right....
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