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The Tempered Aspirations solution for bargaining problems with a reference point

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  • Balakrishnan, P.V. (Sundar)
  • Gómez, Juan Camilo
  • Vohra, Rakesh V.

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.

Suggested Citation

  • Balakrishnan, P.V. (Sundar) & Gómez, Juan Camilo & Vohra, Rakesh V., 2011. "The Tempered Aspirations solution for bargaining problems with a reference point," Mathematical Social Sciences, Elsevier, vol. 62(3), pages 144-150.
  • Handle: RePEc:eee:matsoc:v:62:y:2011:i:3:p:144-150
    DOI: 10.1016/j.mathsocsci.2011.09.003
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    References listed on IDEAS

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    1. Bossert, Walter & Nosal, Ed & Sadanand, Venkatraman, 1996. "Bargaining under Uncertainty and the Monotone Path Solutions," Games and Economic Behavior, Elsevier, vol. 14(2), pages 173-189, June.
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    1. repec:eee:ijrema:v:29:y:2012:i:3:p:280-291 is not listed on IDEAS
    2. Emin Karagözoğlu & Kerim Keskin, 2015. "A Tale of Two Bargaining Solutions," Games, MDPI, Open Access Journal, vol. 6(2), pages 1-14, June.

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