Between anchors and aspirations: a new family of bargaining solutions

Abstract

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.

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“…An important difference between the bargaining advantages provided by these two approaches is that the former can be exercised unilaterally, whereas the latter needs to be mutually acknowledged. In that sense, the power provided by the disagreement point can be labeled as hard power, whereas the power provided by the reference point can be labeled as soft power [11].…”

“…This gives us a unifying framework for the study of bargaining problems with a reference point. [11]. The collection of all such solutions (for which 0 ≤ α, β ≤ 1) constitutes the (α, β)-family of bargaining solutions [11].…”

“…[11]. The collection of all such solutions (for which 0 ≤ α, β ≤ 1) constitutes the (α, β)-family of bargaining solutions [11]. In bargaining problems, the two parameters α and β with a reference point allow us to obtain a family of bargaining solutions.…”

“…This bargaining solution is the LKSBS. Naturally, in between these four corner cases, there are infinitely many intermediate solution concepts that propose settlements by offering feasible compromises between the worst case and the best case scenarios described by anchors and aspirations, respectively [11].…”

“…By using the α, β ∈ [0, 1] factors, we define the (α, β)-solution where α can be interpreted as the power of the reference point in determining the anchor point, and β can be interpreted as the influence of the reference point in shaping players' aspirations. For every (S, d, r) ∈ n , the bargaining solution with a given (α,β) ∈ [0, 1] 2 F α,β (S, d, r) is defined as follows [11];…”