Think about an ultimatum game in which the proposer divides $10 and the recipient decides whether to accept or reject the proposal. If the recipient rejects the proposal, neither player receives anything. Let's use F to stand for the absolute value of the difference between the two players' payoffs, as in Problem 8. Suppose the proposer is selfish and cares only about his own dollar payoff. The receiver, however, cares about fairness-she ranks the outcomes according to the value U(R,F) =R - 0.5F, where R is her dollar payoff. Which proposals will she accept? Which ones will she reject? Knowing that information, what will the proposer offer?