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Recent laboratory studies of alternating-offer bargaining find many empirical regularities that are inconsistent with the standard theory. In this paper, the author postulates that bargainers behave as if they are negotiating over both "absolute" and "relative" money. Absolute money is measured by cash, relative money by the disparity between absolute measures. The resulting model is consistent with previously observed regularities. New experiments provide further support as well as evidence against several alternative explanations. Also finding some support is an extension that predicts that the equilibrium of the standard theory will be observed when bargaining is done in a "tournament" setting. Copyright 1991 by American Economic Association.