You must completely answer the following questions as well as supply proof of your assertion that your chosen locations are Nash equilibriums as well as the Socially Optimal location. So a statement that a point is Nash equilibrium (NE) without proof will be considered wrong. Note: There can situations where 1 NE exists or no NE exists, so be careful. When you answer the question, the diagram I used in class will be Very helpful in getting your point across to me.

Consumers are located uniformly along a straight 1 mile road that leads from the one end of town to the other (no cross roads exists). Each consumer wants to buy one unit of a good from an existing store. The transportation cost or the cost of walking to an individual firm is proportional to the distance the consumer must travel to the store (i.e. If the consumer is located at the point .4 and the store is located at 1, the cost of transportation is 0.6). The law prohibits competition between the stores through price so that the same good must be sold at the each store for the same price. The only way to compete within the model is through the choice of location along the 1 mile stretch of road. The profits received by any store are only determined by the number of customers each store receives due to its location. This implies that if multiple stores locate at the same location, they split the profits (or customers) evenly.

Definitions:
1) Nash equilibrium-any combination of strategies in which each player's strategy is his or her best choice, given the other players' choices.
2) Socially optimal-a combination (choice of placement of store) that minimizes the cost to the individual consumers located on the road.