(8 Points) Imagine a continuum of potential buyers, located on the line segment [0, 1], with uniform distribution. (Hence the \"mass\" or quantity of buyers in the interval [a, b] is equal to ba.) Imagine two firms, players 1 and 2, who are located at each end of the interval (player 1 at the 0 point and player 2 at the 1 point). Each player i can choose its price pi, and each customer goes to the vendor who offers him the highest value. However, price alone does not determine the value; distance is important as well. In particular each buyer who buys the product from player i has a net value of v-pi-di , where di is the distance between the buyer and vendor i and represents the transportation costs of buying from vendor i. Thus buyer a [0, 1] buys from 1 and not 2 if v-p1-di>v-p2-d2 and if buying is better than getting zero. (Here d1 = a and d2 = 1 a. The buying choice would be reversed if the inequality were reversed.) Finally, assume that the cost of production is zero. (1) What is the best-response function of each player? (2) Assume that v = 1. What is the Nash equilibrium? Is it unique? 3) Now assume that the trapsportation costs are 3a!i , so that a buyer buys from 1 if and only if v p; p > y y y p %dl >vp; %dz. Write down the best-response function of each player and solve for the Nash equilibrium. (1) Best-response function of each player: To find the best-response function for each player, we need to determine the price that maximizes their profit given the strategies of the other player. Let's start with player 1 (located at point 0). A buyer located at position a will choose player 1if the following condition holds: vpa>vp(1a) pta

vpa m+(1-a)