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

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  • Lombardi, Michele
  • Yoshihara, Naoki

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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Bibliographic Info

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

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Length: 10, [1] p.
Date of creation: Jul 2008
Date of revision:
Handle: RePEc:hit:hituec:a501

Note: June, 2008
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Keywords: Bargaining problems; claims point; proportional solution; nonconvexity; solidarity axioms;

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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. Marco Mariotti, 1998. "Fair Bargains: Distributive Justice and Nash Bargaining Theory," Royal Holloway, University of London: Discussion Papers in Economics 98/16, Department of Economics, Royal Holloway University of London, revised Feb 1998.
  3. Thomson, W., 1989. "Cooperative Models Of Bargaining," RCER Working Papers 177, University of Rochester - Center for Economic Research (RCER).
  4. Naoki Yoshihara, 2000. "Characterizations of Bargaining Solutions in Production Economies with Unequal Skills," Discussion Paper Series a396, Institute of Economic Research, Hitotsubashi University.
  5. 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.
  6. Nash, John, 1950. "The Bargaining Problem," Econometrica, Econometric Society, vol. 18(2), pages 155-162, April.
  7. Kalai, Ehud & Smorodinsky, Meir, 1975. "Other Solutions to Nash's Bargaining Problem," Econometrica, Econometric Society, vol. 43(3), pages 513-18, May.
  8. 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.
  9. 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.
  10. 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.
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Cited by:
  1. Xu, Yongsheng & Yoshihara, Naoki, 2011. "Proportional Nash solutions - A new and procedural analysis of nonconvex bargaining problems," Discussion Paper Series 552, Institute of Economic Research, Hitotsubashi University.

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