Suppose that a section of beach facing east has one pier to the north and another pier one mile south of the first one. Two ice cream vendors (N and S) are considering where to place their carts in this one-mile stretch between the piers. Assume that 800 beachgoers are distributed evenly along the beach between the piers. Also assume that all beachgoers like ice cream equally and are indifferent between either of these two vendors. They will simply go to the cheaper vendor, or to the closer vendor if the vendors charge the same price. Assume that these two vendors charge the same price, so their only way to distinguish themselves is their location. Suppose that local ordinances dictate that the vendors can only choose positions at the north pier, 1⁄4 mile from the north pier, 1/2 mile from the north pier, 3⁄4 mile from the north pier, and at the south pier (1 mile from the north pier). Also suppose that if both vendors choose the same location, vendor N will choose a position that is just barely north of vendor S’s position, meaning that all customers to the north of the two vendors will choose N, and all customers to the south will choose S. Note that this is only true if they choose the same location, as customers always go to the closer of the two vendors.

a. Suppose that the vendors choose their locations simultaneously. Then this is a simultaneous move game with the following matrix:

0 1/4 1/2 3/4 1
0
1/4
1/2
3/4
1

b. Now assume that instead of a completely uniform distribution of beachgoers

across the entire section of beach, 600 beachgoers are distributed evenly along the northern half of this section, and 200 beachgoers are distributed evenly along the southern half. All other assumptions remain the same. Draw a new picture representing this different version of the game. Fill in the matrix below with the new payoffs and find the Nash Equilibria.

0 1/4 1/2 3/4 1
0
1/4
1/2
3/4
1

c. How does this model provide insight into the location choices of CVS and Walgreens, gas stations, or restaurants?
d. How does this model provide insight into political campaign positioning, particularly moving between party and general elections?