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The Tempered Aspirations solution for bargaining problems with a reference point

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

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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Article provided by Elsevier in its journal Mathematical Social Sciences.

Volume (Year): 62 (2011)
Issue (Month): 3 ()
Pages: 144-150

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Handle: RePEc:eee:matsoc:v:62:y:2011:i:3:p:144-150
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  1. Chun, Youngsub & Thomson, William, 1992. "Bargaining problems with claims," Mathematical Social Sciences, Elsevier, vol. 24(1), pages 19-33, August.
  2. Thomson, William, 1983. "Problems of fair division and the Egalitarian solution," Journal of Economic Theory, Elsevier, vol. 31(2), pages 211-226, December.
  3. Moulin, Herve, 1985. "Egalitarianism and Utilitarianism in Quasi-linear Bargaining," Econometrica, Econometric Society, vol. 53(1), pages 49-67, January.
  4. Thomson, William, 1987. "Monotonicity of bargaining solutions with respect to the disagreement point," Journal of Economic Theory, Elsevier, vol. 42(1), pages 50-58, June.
  5. Chun, Youngsub & Thomson, William, 1990. "Nash solution and uncertain disagreement points," Games and Economic Behavior, Elsevier, vol. 2(3), pages 213-223, September.
  6. Lensberg, Terje, 1988. "Stability and the Nash solution," Journal of Economic Theory, Elsevier, vol. 45(2), pages 330-341, August.
  7. Bossert, Walter, 1992. "Monotonic solutions for bargaining problems with claims," Economics Letters, Elsevier, vol. 39(4), pages 395-399, August.
  8. Sunil Gupta & Zvi A. Livne, 1988. "Resolving a Conflict Situation with a Reference Outcome: An Axiomatic Model," Management Science, INFORMS, vol. 34(11), pages 1303-1314, November.
  9. P. V. (Sundar) Balakrishnan & Jehoshua Eliashberg, 1995. "An Analytical Process Model of Two-Party Negotiations," Management Science, INFORMS, vol. 41(2), pages 226-243, February.
  10. Chun, Youngsub & Thomson, William, 1990. "Bargaining with Uncertain Disagreement Points," Econometrica, Econometric Society, vol. 58(4), pages 951-59, July.
  11. Myerson, Roger B, 1981. "Utilitarianism, Egalitarianism, and the Timing Effect in Social Choice Problems," Econometrica, Econometric Society, vol. 49(4), pages 883-97, June.
  12. Carmen Herrero & Antonio Villar, 2009. "The Rights-Egalitarian Solution for NTU Sharing Problems," Working Papers 09.01, Universidad Pablo de Olavide, Department of Economics.
  13. Ehud Kalai, 1977. "Proportional Solutions to Bargaining Situations: Interpersonal Utility Comparisons," Discussion Papers 179, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  14. Bossert, Walter, 1993. "An alternative solution to bargaining problems with claims," Mathematical Social Sciences, Elsevier, vol. 25(3), pages 205-220, May.
  15. Chun, Youngsub & Thomson, William, 1990. "Egalitarian solutions and uncertain disagreement points," Economics Letters, Elsevier, vol. 33(1), pages 29-33, May.
  16. Nash, John, 1950. "The Bargaining Problem," Econometrica, Econometric Society, vol. 18(2), pages 155-162, April.
  17. 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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