Consumers distributed uniformly along a straight-line road are the potential market for two duopoloists whose decision problem is where to locate their sales offices. Demand is completely inelastic, and consumers will purchase from whichever sales office is nearer. Assume that the road is 4 miles long and that, for simplicity, each firm has exactly five possible strategies: it may locate itself at either end or at the 1-mile, 2-mile, or 3-mile markets. Let the payoffs to the duopolists be their respective market shares. (a) Is this a zero-sum (or constant-sum) game? (b) What is the payoff matrix? (c) What are optimal strategies for the duopolists?