Please use game theory knowledge to solve the following problems, preferably with detailed steps, thank you very much!

5. Consider a beach of unit length (think about it as an interval [0, 1]). Two vendors of ice-cream simultaneously decide where to locate themselves: they will each pick a number in [0, 1] as location on the beach. Assume that there are continuously infinite consumers and they are uniformly distributed on the beach and will just go to the nearest vendor. For example, if vendor 1 is located at 0.3 and vendor 2 is located at 0.8, then vendor 1 gets the consumers on [0, 0.55) and vendor 2 gets the consumers on (0.55, 1). Each vendor's goal is to attract as many consumers as possible. Find all the NE of this game and show your reasoning