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.For the contract to make Dean's promise credible,the value of the penalty must be
A) any positive number.
B) more than $1.5 million.
C) less than $100.
D) more than $500,000.
E) more than $500.

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.For the contract to make Dean's promise credible,the value of the penalty must be
A) any positive number. 
B) more than $1.5 million. 
C) less than $100. 
D) more than $500,000. 
E) more than $500.

Quizplus · Accepted Answer

If Dean signs a legally-binding contract that penalizes him if he fails to choose the upper branch at Y or Z, he essentially removes the possibility of choosing the lower branches at Y or Z. Therefore, the decision tree from Matthew's perspective changes to a simple two-option scenario where he either chooses X or Y. In this case, choosing Y guarantees Matthew a payoff of $1.5 million, while choosing X only guarantees him a payoff of $1 million. Therefore, he should choose Y.

The value of the penalty must be large enough to ensure that Dean has an incentive to choose the upper branch at Y or Z. If the penalty is too low, he could still choose the lower branch and pay the penalty without losing too much of his expected payoff. Based on the given payoffs, a penalty of $500,000 would be enough to make the contract credible, as choosing the lower branch at Y or Z would result in a loss of $1 million for Dean. Therefore, D is the correct answer.

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