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. If before Tracy chose, Amy could make a credible commitment to choose either the top or bottom branch when her turn came, then we would expect Tracy to get a payoff of ________ and Amy to get a payoff of ________.
A)25; 225
B)300; 200
C)75; 150
D)125; 125

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.  If before Tracy chose, Amy could make a credible commitment to choose either the top or bottom branch when her turn came, then we would expect Tracy to get a payoff of ________ and Amy to get a payoff of ________.
A)25; 225 
B)300; 200 
C)75; 150 
D)125; 125

Quizplus · Accepted Answer

If Amy commits to choosing the top branch, then Tracy will choose the bottom branch and Amy will get 150, but if Amy commits to choosing the bottom branch, then Tracy will choose the top branch and Amy will get 200. So, it's in Amy's interest to commit to the bottom branch, and Tracy will respond by choosing the top branch.

Tracy and Amy Are Playing a Game in Which Tracy