Along a stretch of beach are 500 children of 100 each (Labeled in clusters A,B,C,D,E, in...

Along a stretch of beach are 500 children of 100 each (Labeled in clusters A,B,C,D,E, in that order.) Two ice-cream vendors are deciding simultaneously where to locate. They must choose the exact location of one of the clusters. If there is a vendor in a cluster, all 100 children will buy an ice-cream. For clusters without a vendor, 50 out of the 100 children are willing to walk to a vendor one cluster away, only 20 are willing to walk to a vendor two clusters away, and none are willing to walk to a vendor three or more clusters away. The ice-cream melts quickly, so the walkers cannot buy for nonwalkers. If the two choose the same clusters, each will get a 50% share of the total demand for ice cream. If they choose different clusters, then those children (locals and walkers) for whom one vendor is closer than the other will go to the closer one, and those for whom the two are equidistant will split 50% each. Each vendor seeks to maximize her sales.

a. Construct a five-by-five matrix for their location game; the entries stated here will give you a start and a check on your calculations:

• If both vendors choose to locate at A, each sells 85 units.

• If the first vendor chooses B and the second chooses C, the first sells 150 and the second sells 170.

• If the first vendor chooses E and the second chooses B, the first sells 150 and the second sells 200.

b. Eliminate dominated strategies as far as possible and find the NEPS

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Expert Solution

Rahul Sunny answered 1 year ago

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