Question

Suppose that there are customers distributed evenly across a line which runs from 0 to 1. There are two competing vendors that choose where on the line to locate. Customers buy from whichever vendor is closest to their location. If the first vendor is located at 1/3, what is the best response for the second vendor?

a. 2/3
b. 1/2
c. Slightly to the left of 1/3
d. Slightly to the right of 1/3

Answer 1

a. 2/3

Step-by-step explanation:

The best response for second vendor is to locate at (1/3) position only because this way, it will be maximizing it's payoff .

Because first vendor serves all customers to left of (1/3) , It's market share is (1/3).

Now if second vendor locates at (1/3) , then it will get the entire market share to right hand side of (1/3) , which is (2/3) share.

Therefore, The best response for the second vendor is 2/3