Imagine a one-dimensional city one mile long, with boundaries at 0 and 1, with a uniform population density of 10,000 people per mile -meaning that the population of the city is 10,000, and that in any segment of length L miles, where 0 lessthanorequalto L lessthanorequalto 1, there are 10,000L customers. Each person buys one bottle of pop every day, at a price of $1 per bottle, a price that is fixed by the city government. There are two pop stores, each can produce and sell pop at a cosot of $.20 per bottle, and each wants to maximize profit. Because they are lazy, people buy their pop from the nearest store. Store One gets to choose its location S_1 first, and then store Two gets to choose its location There are 3 possible locations, 0, 1/2 and 3/4. Two stores cannot occupy the same location, (a) construct the game tree for this game; (b) find the subgame perfect Nash equilibrium.