Tracy and Amy are playing a game in which Tracy has the first move at X in the decision tree shown below. Once Tracy has chosen either the top or bottom branch at X, Amy, who can see what Tracy has chosen, must choose the top or bottom branch at Y or Z. Both players know the payoffs at the end of each branch. In the equilibrium of this game:
A)Tracy and Amy both get 125.
B)Tracy gets 75 and Amy gets 150.
C)Tracy gets 300 and Amy gets 200.
D)Tracy gets 25 and Amy gets 225.

Question

Tracy and Amy are playing a game in which Tracy has the first move at X in the decision tree shown below. Once Tracy has chosen either the top or bottom branch at X, Amy, who can see what Tracy has chosen, must choose the top or bottom branch at Y or Z. Both players know the payoffs at the end of each branch.  In the equilibrium of this game:
A)Tracy and Amy both get 125. 
B)Tracy gets 75 and Amy gets 150. 
C)Tracy gets 300 and Amy gets 200. 
D)Tracy gets 25 and Amy gets 225.

Quizplus · Accepted Answer

Tracy knows that Amy will always choose the top branch, so if Tracy chooses the top branch she will earn 25, and if she chooses the bottom branch she will earn 75. So Tracy will choose the bottom branch, and then Amy will choose the bottom branch.

Tracy and Amy Are Playing a Game in Which Tracy