Between anchors and aspirations: a new family of bargaining solutions

We study the salience and power of reference points in determining the effective anchors and aspirations in bargaining problems. Along this line, we enrich the analysis of the standard bargaining model with two new parameters: the first parameter can be interpreted as the effectiveness (or salience) of the reference point in determining the anchor, whereas the second parameter can be interpreted as its effectiveness in shaping agents’ aspirations. Utilizing these parameters, we provide a unifying framework for the study of bargaining problems with a reference point. The two-parameter family of bargaining solutions we obtain encompasses some well-known solutions as special cases. We offer multiple characterizations for each individual member of this family as well as two characterizations for the whole solution family in bilateral bargaining problems.