A tale of two bargaining solutions
We set up a rich bilateral bargaining model with four salient points (disagreement point, ideal point, reference point, and tempered aspirations point), where the disagreement point and the utility possibilities frontier are endogenously determined. This model allows us to compare two bargaining solutions that use reference points, the Gupta-Livne solution and the tempered aspirations solution, in terms of Pareto efficiency in a strategic framework. Our main result shows that the weights solutions place on the disagreement point do not directly imply a unique efficiency ranking in this bargaining problem with a reference point. In particular, the introduction of a reference point brings one more degree of freedom to the model which requires also the difference in the weights placed on the reference point to be considered in reaching an efficiency ranking.