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Two equally competitive pet shops want to locate stores in

Lake Tahoe, where there are...
Two equally competitive pet shops want to locate stores in Lake Tahoe, where there are currently none. There are three main business centers. Tahoe City serves 34% of the population, Incline Village 16%, and South Lake Tahoe 50%. If both shops locate in the same center, they split all the business equally, if they located in different centers, they each get all the business in the center in which they locate plus half the business in the third center. Where should the pet shops locate? Set up a game matrix and solve.
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Answered in 42 minutes by:
10/19/2013
Ray Atkinson
Ray Atkinson, Bachelor's Degree
Category: Math Homework
Satisfied Customers: 1,890
Experience: Inner-city high school substitute teacher. Degrees in mathemetics, accounting, and education. Years and years of tutoring.
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Ray Atkinson :

What is the deadline for this, please?

Ray Atkinson :

The key is to only care about what shop #1 is going to get. If they both go to the same town, they each get 50%. If #1 goes to one town and #2 goes to another, #1 gets all of that town, and half of the third town.

Ray Atkinson :

If #1 goes to Tahoe, #2 can go to Tahoe and #1 gets 50%. If they go to Incline, #1 gets all 34 from Tahoe and half of the 50 from South. 34+(50/2)=59.
Similarly, if #2 goes to South, #1 gets 34+(16/2)=42.

Ray Atkinson :

Next line.

Ray Atkinson :

#1 goes to Incline, #2 goes to Tahoe. 16+(50/2)=41
Both go to Incline, each get 50.
#2 goes to South, #1 gets 16+(34/2)=33

Ray Atkinson :

Last line.

Ray Atkinson :

#1 goes to South, #2 to Tahoe. #1 gets 50+(16/2)=58.
#2 goes to Incline. #1 gets 50+(34/2)=67
Both go to South, each gets 50.

Ray Atkinson :

Now, both stores know all the facts. They can both read that same chart.

Ray Atkinson :

#1 is going to read each column (store #2's choices) and pick the best one for #1. The highest number in each column is for store #1 to choose South Lake Tahoe. 58 is the best choice if #2 goes to Tahoe, 67 is the best if #2 goes to Incline, and 50 is the best if #2 goes to South.

Ray Atkinson :

Like I said, #2 can see these numbers as well. They see that their choices are going to be to choose store #1 to get 58%, 67%, or 50% of the business. Their best option is to only let #1 get 50% of the business, so they are going to choose South like store #1 did.

Both stores will open up in South Lake Tahoe and split the business evenly.

Customer:

Thank you very much

Ray Atkinson
Ray Atkinson, Bachelor's Degree
Category: Math Homework
Satisfied Customers: 1,890
Experience: Inner-city high school substitute teacher. Degrees in mathemetics, accounting, and education. Years and years of tutoring.
Verified
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Ray Atkinson
Ray Atkinson
Ray Atkinson, Bachelor's Degree
Category: Math Homework
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Experience: Inner-city high school substitute teacher. Degrees in mathemetics, accounting, and education. Years and years of tutoring.

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