2. Suppose ice cream consumers are distributed along a straight beach of 1km. Each consumer buys 1 ice cream from the closest ice cream cart. If carts are equidistant from a consumer, he will buy from each of them with equal probability. We have seen in lecture what the Nash equilibrium is if 2 carts simultaneously choose where to position themselves. Now suppose there are 3 ice cream carts simultaneously deciding where to position themselves. Is it a Nash equilibrium for all 3 to position themselves where the median consumer is located? (Explain in no more than two short sentences)