Consider an ultimatum game, where the proposer (P) offers the responder (R) a split, (SP, SR), of a $100 endowment. Suppose further that each individual's utility, defined over money (M), is given by ui = 2√M, i = {P, R}. Suppose now that this game becomes a dictator game. Find the utility possibilities frontier (UPF) for this game, and represent it in the (UP, UR) -space.