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

  • Michele Lombardi

    (Queen Mary, University of London)

  • Naoki Yoshihara

    ()

    (Hitotsubashi University)

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 Queen Mary University of London, School of Economics and Finance in its series Working Papers with number 632.

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Date of creation: Jul 2008
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Handle: RePEc:qmw:qmwecw:wp632
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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.
  2. Nash, John, 1950. "The Bargaining Problem," Econometrica, Econometric Society, vol. 18(2), pages 155-162, April.
  3. Yoshihara, Naoki, 2003. "Characterizations of bargaining solutions in production economies with unequal skills," Journal of Economic Theory, Elsevier, vol. 108(2), pages 256-285, February.
  4. Marco Mariotti, 1999. "Fair Bargains: Distributive Justice and Nash Bargaining Theory," Review of Economic Studies, Oxford University Press, vol. 66(3), pages 733-741.
  5. 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.
  6. 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.
  7. Chun, Y. & Thomson, W., 1989. "Bargaining Problems With Claims," RCER Working Papers 189, University of Rochester - Center for Economic Research (RCER).
  8. Marco Mariotti, 1998. "Nash bargaining theory when the number of alternatives can be finite," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 15(3), pages 413-421.
  9. Yongsheng Xu & Naoki Yoshihara, 2008. "The Behaviour Of Solutions To Bargaining Problems On The Basis Of Solidarity," The Japanese Economic Review, Japanese Economic Association, vol. 59(1), pages 133-138.
  10. 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.
  11. Kalai, Ehud & Smorodinsky, Meir, 1975. "Other Solutions to Nash's Bargaining Problem," Econometrica, Econometric Society, vol. 43(3), pages 513-18, May.
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