In a study of alternating offer bargaining with discounting, perfect equilibrium was found to have little predictive power, under the conventional assumption that bargainers' utility is measured by their monetary payoffs. Instead, our data exhibit a first-mover advantage, independent of the equilibrium prediction. However the pattern of rejected offers and counterproposals shows bargainers' utility was not measured by their monetary payoffs: 81 percent of rejected offers were followed by counterproposals that would earn less money. We also reanalyze data from earlier experiments, finding a similar pattern of rejections and counterproposals.

The college admissions problem is perhaps the simplest model of many-to-one matching in two-sided markets, such as labor markets. The authors show that the set of stable outcomes (which is equal to the core defined by weak domination) has some surprising properties not found in models of one-to-one matching. These properties may help to explain the success that this kind of model has had in explaining empirical observations.