Consider the ice-cream sellers' problem based on the Hotelling model. Specifically, two ice-cream vendors sell identical products and have to simultaneously decide where to locate themselves to maximise their respective sales. The potential customers are assumed to be distributed uniformly on the [0,1] segment (unit interval). Hence, a choice of location for each vendor would be a number between 0 and 1 (including the two extremes).

i. Describe clearly why a choice of 0 by one vendor and a choice of 1 by the other is not an equilibrium outcome. In other words, argue that (0,1) is not a Nash equilibrium.

ii. Recall the Median Voter Theorem. Is there a parallel between the Median Voter Theorem and this ice-cream vendor game?