Research on ultimatum and dictator games has found that because of ''fairness'' first movers in such games offer more than noncooperative game theory predicts. We find that if the right to be the first mover is ''earned'' by scoring high on a general knowledge quiz, then first movers behave in a more self-regarding manner. We also conducted dictator double blind experiments, in which the experimenter could not identify the decision maker. The results yielded by far our largest observed incidence of self-regarding offers, suggesting that offers are due to strategic and expectation considerations. Journal of Economic Literature Classification Numbers: C78, C91. (C) 1994 Academic Press, Inc.