A Tale of Two Bargaining Solutions

Abstract

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.

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“…Recently, there has been an increased interest in the experimental investigation of reference point effects in bargaining problems [10]. The reference integrative bargaining situation (RIBS) is one of the first studies which incorporated the notion of a reference point into the simple bargaining model.…”

“…It is important to note that the reference point outcome does not replace the conflict outcome because each player can still veto any agreement, forcing the players to obtain their conflict payoffs. Instead, the reference point outcome is an additional important factor in determining the final outcome [10]- [11].…”

“…In the RIBS, another salient point, called the ideal point ℐ( , ) ∉ , is employed. Originally, it was introduced by Kalai and Smorodinsky to represent an outcome in which each player is awarded the maximum utility he can hope to achieve, assuming that the other players will never accept outcomes which are worse for them than the conflict outcome [10]. Usually, ideal point is infeasible in the bargaining problem.…”

“…The RIBS on ∑ is a function that associates with each triple ( , , ) ∈ ∑ a unique outcome RIBS ( , , ) ∈ . Mathematically, it can be formally defined as follows [10]- [11];…”

“…Technically, the RIBS provides the maximum point of the feasible set on the line segment connecting the ℐ( , ) point and the point. Therefore, it is the intersection point of the Pareto frontier of and that line segment [10]. This is equivalent to saying that the RIBS selects the maximum individually rational payoff profile at which each player's payoff gain from his reference point has the same proportion to the payoff difference between his ideal point and his reference point.…”