Assume a town that stretches out along a main road that is 1 mile long. There are two companies (A & B) that have decided to open up gas stations along this mile stretch.

Assume that customers are uniformly distributed along the mile and that they have no preference for one brand of gasoline over the other. Customers will simply purchase from the gas station that is closest to them. Where should each company set their gas station if they are to attract the most customers?

(Picture a straight line, with a line in the middle indicating 0.5 -- Now, where should A & B gas stations be located within that mile?)

Assume next that the two gas stations compete by setting their price. Since there is no notable difference between the two brands of gasoline, customers will purchase gas from the station with the cheapest prices. Each gas station has two possible strategies: High Price or Low Price. The market value at a high price is $900,000. The market value at a low price is $500,000. When both stations charge the same price, each station gets 50% of the customers and consequently 50% of the market value. Construct a matrix for the game between both gas stations. Make sure to identify the players, the strategies and the payoffs.

Find the Nash Equilibrium of the game and explain why your result is the equilibrium. If the Nash Equilibrium the best outcome for the game? If not, explain how this outcome can be improved.