Suppose you are playing the game of rock-paper-scissors with your friend. As we saw in

class, there are three possible outcomes: win (W), lose (L), or draw (D). If you have a

utility function u which assigns payoffs to each outcome:

(a) (5 points) We call a relationship ordinal if only the order matters. How many

ordinal preference relationships can there be in this game, if you are never indifferent

(i.e. placed the same utility on) between outcomes?

(b) (5 points) Give an explanation of what kinds of preferences would create rela-

tionship like u(W) < w(D) < u(L). What about u(D) > u(L) = u(W)?