Could someone please help me with a step by step instructions on how to find nash equilibriums? Also how do i show the nash equilibriums I find?

Exercise 4. Continuous Came: Hotelling's Model Two ice cream vendors are on a beach that stretches the 0-1 interval. Customers are uniformly dis- tributed along that interval. The vendors simultaneously select their positions, that is, their strategies are v1 6 [0,1] and v2 6 [0,1]. Customers go to the closest vendor and split themselves evenly if the vendors choose an identical position. Each vendors want to maximize its number of customers. a. Show that choosing locations v1 = 1/2 and v2 = 1/ 2 is a Nash Equilibrium. b. Show that the Nash Equilibrium in a. is the unique Nash Equilibrium in pure strategies. c. Now consider the same problem with four vendors. If they choose locations v1 2 v2 = 1/4 and v3 2 v4 = 3/4, show that their market shares are 1/4 each. d. Show that the strategy prole described in c. is a Nash Equilibrium when there are four vendors