Suppose you are on a Boardwalk where tourists are evenly distributed on the road that is one mile long. Three hot dog vendors simultaneously chose where to locate to maximize their own market share. Tourists prefer to buy from the closer hot dog vendor. Only one hot dog vendor can be picked.

1) What is the Nash equilibrium that all three hot dog vendors locate in the middle on the road?

2) What is the Nash equilibrium that they locate at 1/6, 1/2 and 5/6 of a mile so that they each share the market?

3) Suppose that its a mall location and the hot dog vendors are in a circular hallway where the circumference is one mile. Compare the circular hallway to the one mile long road in question 2.