In the above decision tree,Matthew picks first and Dean picks second.Matthew and Dean both know the payoffs to each choice for both themselves and each other.
-Refer to the decision tree above.Suppose Dean promises Matthew that he will always select the upper branch at either Y or Z.Dean offers to sign a legally-binding contract that penalizes him if he fails to choose the upper branch at Y or Z.The penalty is $250.The outcome of the game is that
A) Matthew picks Z and Dean pays the fine.
B) Matthew picks Y and Dean does not pay the fine.
C) Matthew picks Z and Dean does not pay the fine.
D) Matthew picks Y and Dean pays the fine.
E) Matthew picks Z and Dean selects the upper branch.

Question

In the above decision tree,Matthew picks first and Dean picks second.Matthew and Dean both know the payoffs to each choice for both themselves and each other.
-Refer to the decision tree above.Suppose Dean promises Matthew that he will always select the upper branch at either Y or Z.Dean offers to sign a legally-binding contract that penalizes him if he fails to choose the upper branch at Y or Z.The penalty is $250.The outcome of the game is that
A) Matthew picks Z and Dean pays the fine. 
B) Matthew picks Y and Dean does not pay the fine. 
C) Matthew picks Z and Dean does not pay the fine. 
D) Matthew picks Y and Dean pays the fine. 
E) Matthew picks Z and Dean selects the upper branch.

Quizplus · Accepted Answer

If Dean keeps his promise, he will select the upper branch at Y and Matthew will receive a payoff of $500. However, if Dean breaks his promise and selects the lower branch at Y, Matthew will receive only $200. Given this, Matthew has an incentive to choose Y to protect himself against the risk of Dean breaking his promise. On the other hand, if Matthew chooses Z, he will receive $100 regardless of what Dean does. Thus, the best strategy for Matthew is to choose Y. Given this, the best strategy for Dean is to keep his promise and choose the upper branch at Y, otherwise he will end up paying the fine. Therefore, the outcome is that Matthew picks Y and Dean pays the fine (Option D).

In the Above Decision Tree,Matthew Picks First and Dean Picks