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

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  • Michele Lombardi

    (Queen Mary, University of London)

  • Naoki Yoshihara

    ()
    (Hitotsubashi University)

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 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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Keywords: Bargaining problems; Claims point; Proportional solution; Nonconvexity; Solidarity axioms;

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  1. Nash, John, 1950. "The Bargaining Problem," Econometrica, Econometric Society, vol. 18(2), pages 155-162, April.
  2. Kalai, Ehud & Smorodinsky, Meir, 1975. "Other Solutions to Nash's Bargaining Problem," Econometrica, Econometric Society, vol. 43(3), pages 513-18, May.
  3. Chun, Youngsub & Thomson, William, 1992. "Bargaining problems with claims," Mathematical Social Sciences, Elsevier, vol. 24(1), pages 19-33, August.
  4. 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.
  5. 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.
  6. 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.
  7. Thomson, W., 1989. "Cooperative Models Of Bargaining," RCER Working Papers 177, University of Rochester - Center for Economic Research (RCER).
  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. Kalai, Ehud, 1977. "Proportional Solutions to Bargaining Situations: Interpersonal Utility Comparisons," Econometrica, Econometric Society, vol. 45(7), pages 1623-30, October.
  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," CCES Discussion Paper Series 42, Center for Research on Contemporary Economic Systems, Graduate School of Economics, Hitotsubashi University.

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