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A New Insight into Three Bargaining Solutions in Convex Problems

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Yongsheng Xu
Naoki Yoshihara

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Abstract

We reconsider the three well-known solutions: the Nash, the egalitarian and the Kalai-Smorodinsky solutions, to the classical domains of convex bargaining problems. A new proof for the Nash solution that highlights the crucial role the axiom Contraction Independence plays is provided. We also give new axiomatic characterizations for both the egalitarian and the Kalai-Smorodinsky solutions. Our results focus on both contraction and expansion independence properties of bargaining problems and, as a consequence, some new insights on the three solutions from the perspective of rational choice may be derived.

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Paper provided by Institute of Economic Research, Hitotsubashi University in its series Discussion Paper Series with number a453.

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Date of creation: Jul 2004
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Handle: RePEc:hit:hituec:a453

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  1. Kalai, Ehud & Smorodinsky, Meir, 1975. "Other Solutions to Nash's Bargaining Problem," Econometrica, Econometric Society, vol. 43(3), pages 513-18, May. [Downloadable!] (restricted)
  2. Kalai, Ehud, 1977. "Proportional Solutions to Bargaining Situations: Interpersonal Utility Comparisons," Econometrica, Econometric Society, vol. 45(7), pages 1623-30, October. [Downloadable!] (restricted)
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  3. Nash, John, 1950. "The Bargaining Problem," Econometrica, Econometric Society, vol. 18(2), pages 155-162, April. [Downloadable!] (restricted)
  4. Thomson, William, 1994. "Cooperative models of bargaining," Handbook of Game Theory with Economic Applications, in: R.J. Aumann & S. Hart (ed.), Handbook of Game Theory with Economic Applications, edition 1, volume 2, chapter 35, pages 1237-1284 Elsevier. [Downloadable!] (restricted)
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