EXERCISE 6.1 (Alternative representations of preferences) A decision-maker's pref- erences over the set A = {a, b, c} are represented by the payoff function u for which u(a) = 0, u(b) = 1, and u(c) = 4. Are they also represented by the function v for which v(a) = -1, v(b) = 0, and v(c) = 2? How about the function w for which wa) = w(b) = 0 and w(c) = 8? Sometimes it is natural to formulate a model in terms of preferences and then find payoff functions that represent these preferences. In other cases it is natural to start with payoff functions, even if the analysis depends only on the underlying preferences, not on the specific representation we choose