The Tempered Aspirations solution for bargaining problems with a reference point |
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Affiliation: | 1. WiLab, Department of Electrical and Computer Engineering, University of Tabriz, Iran;2. Electrical and Electronics Engineering Department, Bilkent University, Turkey;1. School of Computer Science and Engineering, Nanjing University of Science and Technology, Nanjing, 210094, China;2. School of Computer and Information Technology, Nanyang Normal University, Nanyang, 473061, China |
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Abstract: | Gupta and Livne (1988) modified Nash’s (1950) original bargaining problem through the introduction of a reference point restricted to lie in the bargaining set. Additionally, they characterized a solution concept for this augmented bargaining problem. We propose and axiomatically characterize a new solution concept for bargaining problems with a reference point: the Tempered Aspirations solution. In Kalai and Smorodinsky (1975), aspirations are given by the so called ideal or utopia point. In our setting, however, the salience of the reference point mutes or tempers the negotiators’ aspirations. Thus, our solution is defined to be the maximal feasible point on the line segment joining the modified aspirations and disagreement vectors. The Tempered Aspirations solution can be understood as a “dual” version of the Gupta–Livne solution or, alternatively, as a version of Chun and Thomson’s (1992) Proportional solution in which the claims point is endogenous. We also conduct an extensive axiomatic analysis comparing the Gupta–Livne to our Tempered Aspirations solution. |
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