Question

Suppose that Jason and Chad each are thinking of opening up a diet coke stand on the fourth floor of this building. Suppose that potential customers are evenly spaced on a distance that is normalized to 1. Customers will buy a diet coke from whichever stand requires the least walking. If they are the same distance the customer will flip a coin. This is depicted below. 314 1/4 1/2 Suppose that Jason and Chad are simultaneously choosing the location of their stands, what is the Nash Equilibrium location? O a. One of them puts a stand at O and the other puts a stand at 1 O b. Chad and Jason put their stands right next to each other at 1/2 c. One of them puts a stand at 3/4 and the other puts a stand at 1/4 O d. There is no Nash Equilibrium

Answer 1

The correct option is B- both put their stands at 1/2 right next to each other.

At this point (1/2), no one has an incentive to move from his location. They would incur loss if they do. Suppose that from 1/2, Jason moves to 3/4 and Chad remains at 1/2. Then Jason would be serving customers between 3/4 to 1 as he is the nearest vendor but for customers between 0 to 1/2, Chad would be the nearest vendor and he would sell to them. For customers between 1/2 to 3/4, both Chad and Jason would be equidistant and they would randomly choose between the two. Thus, Chad would be getting more market share than Jason. Jason can improve his state by moving to 1/2. In this way he would be nearest vendor to people from 1/2 to 1.

We can see that if they both choose any other location, one of they would have an incentive to change their location and increase his market share.

The only Nash would be B.