4. The city of Spider is a strange town with just 3 roads that spike out from a point, C, which is called the town center. The spikes, CX, CY, and CZ are 1 mile each. The map of Spider is shown below. People live uniformly distributed all over the roads and go from any point of the city to another by these roads. Ice-cream vendors in Spider have to decide (each independently) where to set up store. Citizens buy from the nearest ice-cream vendor (breaking ties using equal probability). The aim of each vendor is to maximize the number of customers. X Y C Z (a) Suppose there are two vendors. Is there a Nash equilibrium? If so, describe it. (b) Suppose there are three vendors. Are there any Nash equilibria? If so, describe them and give a brief explanation for your answer. (c) Suppose there are four vendors. Are there any Nash equilibria? If so, describe them and give a brief explanation for your answer. (d) Return to the case of 3 vendors and consider a case where CZ is 2 miles long. Will there be a Nash equilibrium? If so describe it