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Alternative Characterizations of the Proportional Solution for Nonconvex Bargaining Problems with Claims

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Michele Lombardi
Naoki Yoshihara

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Abstract

We provide three alternative characterizations of the proportional solution defined on compact and comprehensive bargaining problems with claims that are not necessarily convex. One characterization result is obtained by using, together with other standard axioms, two solidarity axioms. Another characterization theorem shows that the single-valuedness axiom is dispensable even within the class of nonconvex problems if the standard symmetry axiom is imposed.

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Paper provided by Institute of Economic Research, Hitotsubashi University in its series Discussion Paper Series with number a501.

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Date of creation: Jun 2008
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Handle: RePEc:hit:hituec:a501

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Related research
Keywords: Bargaining problems; claims point; proportional solution; nonconvexity; solidarity axioms;

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Find related papers by JEL classification:
C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory
D60 - Microeconomics - - Welfare Economics - - - General
D70 - Microeconomics - - Analysis of Collective Decision-Making - - - General

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  1. Ross, Stephen A, 1973. "The Economic Theory of Agency: The Principal's Problem," American Economic Review, American Economic Association, vol. 63(2), pages 134-39, May. [Downloadable!] (restricted)
  2. Marco Mariotti, 1998. "Nash bargaining theory when the number of alternatives can be finite," Social Choice and Welfare, Springer, vol. 15(3), pages 413-421. [Downloadable!] (restricted)
  3. Xu, Yongsheng & Yoshihara, Naoki, 2006. "Alternative characterizations of three bargaining solutions for nonconvex problems," Games and Economic Behavior, Elsevier, vol. 57(1), pages 86-92, October. [Downloadable!] (restricted)
  4. Chun, Youngsub & Thomson, William, 1992. "Bargaining problems with claims," Mathematical Social Sciences, Elsevier, vol. 24(1), pages 19-33, August. [Downloadable!] (restricted)
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  5. Mariotti, Marco, 1999. "Fair Bargains: Distributive Justice and Nash Bargaining Theory," Review of Economic Studies, Blackwell Publishing, vol. 66(3), pages 733-41, July. [Downloadable!] (restricted)
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  6. Nash, John, 1950. "The Bargaining Problem," Econometrica, Econometric Society, vol. 18(2), pages 155-162, April. [Downloadable!] (restricted)
  7. Yongsheng Xu & Naoki Yoshihara, 2006. "The Behavior of Solutions to Bargaining Problems on the Basis of Solidarity," Discussion Paper Series a474, Institute of Economic Research, Hitotsubashi University. [Downloadable!]
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  8. 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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