Two competitive pet shops want to open stores at Lake Tahoe, where there are currently no pet shops. The following figure shows the percentages of the total Tahoe population serviced by each of the three main business centers. If both shops open in the same business center, then they split all the business equally; if they open in two different centers, then they each get all the business in the center in which they open plus half the business in the third center. Where should the two pet shops open? Set up a game matrix and solve.

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Tahoe City 20% Lake Tahoe Incline Village 30% South Lake Tahoe 50%