Ives LeFancy and Donna Gabbana are two top fashion designers who own stores on Trendy St. Each has to decide whether to present their "ready-to-wear" collection at the Los Angeles Fashion Week (L.A.) or at the New York Fashion Week (N. Y.) (they can only present at one of them). If Ives chooses L.A. and Donna chooses N.Y., then Ives' (estimated) profits are $160,000 and Donna's are $125,000. If both choose to present in L.A., then Ives' (estimated) profits are $45,000 and Donna's are $30,000. If both choose to present in N.Y., then Ives' (estimated) profits are $55,000 and Donna's are $70,000. And if Ives chooses N.Y. and Donna chooses L.A., then Ives' (estimated) profits are $95,000 and Donna's are $110,000. If they make their choices simultaneously and independently then, using the Nash equilibrium concept, we find that
- The only Nash equilibrium is: Ives chooses L.A. and Donna chooses L.A.
- There are two Nash equilibria: 1) Ives chooses L.A. and Donna chooses L.A.; 2) Ives chooses N.Y. and Donna chooses N.Y.
- The only Nash equilibrium is: Ives chooses L.A. and Donna chooses N.Y.
- None of the above
Decision tree is a reference instrument which is used in the process of decision analysis. It shows the various possible strategies on the branches of the decision tree. It simplifies the problem of decision with its smooth presentation.
Answer and Explanation: 1
If they make their choices simultaneously and independently then, using the Nash equilibrium concept, we find that The only Nash equilibrium is: Ives chooses L.A. and Donna chooses N.Y. .
This is the decision tree which is as follows as per situation.
Donna would prefer N.Y. at node b because she gets the higher payoff at this extent and at node c, she would prefer having L.A. because here the choice of this alternative gives her higher possible payoff.
When Ives is given a choice to choose between these two alternatives, then he would have the following decision tree along with the case of Donna.
Hence, in this diagram, it could be seen that Ives have enough payoff when he chooses L.A. but at the same time at this point, Donna is getting higher payoff when she chooses the alternative of N.Y.
From this diagram, it could be interpreted as Ives would choose L.A while Donna would choose N.Y.
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fromChapter 2 / Lesson 12
Clearly identifying all possible solutions for a given decision is an important part of successful management. In this lesson, you will learn how to use a decision tree to identify and select possible courses of action.