There are two ice cream vendors, Ben and Jerry, on a crowded strip of beach. There are five permissible locations for ice cream vendors to locate, cleverly named positions 1, 2, 3, 4, and 5. Position 1 is at the far north end of the beach, Position 5 at the far south end, and Position 3 in the middle, while Positions 2 and 4 are midway between their respective neighbors. Each location may accommodate more than one vendor. There are 1,000 beachgoers scattered uniformly across the beach (200 at each position) who will buy from the closest vendor.
a. Fill in the payoff matrix on the next page, with payouts reflecting the number of customers each vendor receives. (Example: If Ben is at Position 1 and Jerry is at Position 4, Ben will get 400 beachgoers at locations 1 and 2, and Jerry will get 600 of the beachgoers at Positions 3, 4, and 5.)
b. Find the Nash equilibrium or equilibria in this game. Where are Ben and Jerry likely to end up locating?