Consider a football stadium that has 3 seating sections (S1, S2, S3) in a row. The distance between sections S1 and S2 is the same as the distance between sections S2 and S3. Each of the sections sits 100 people.

Now, consider two hotdog vendors who have to decide the sections in which to set up their shop in order to sell as many hotdogs as possible. Since the fans do not want to miss any part of the game, they will buy from the hotdog vendor in the sections closest to them (assume the distance inside the section does not matter to them). We will also assume that this is a hungry crowd in a popular game, so every seat is occupied and every person will buy one hotdog.

If both the vendors are in equally distant sections, then half the fans buy from one vendor and half from the other. For example, if one vendor is in S1 and one vendor is in S3, half the people in S2 will buy from the first vendor and half from the second vendor. Similarly, if both vendors are in the same section, half of the fans will buy one vendor and half from the other vendor.

a. Construct a payoff matrix showing the payoffs of the vendors for each of their strategies.

b. Is there a dominant strategy for this game? If so, is it strictly dominant?

c. Find the pure-strategy Nash Equilibria of this game.