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Fair bargains: distributive justice and Nash Bargaining Theory

  • Marco Mariotii

    (University of Manchester)

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    The Suppes-Sen dominance relation is a weak and widely accepted criterion of distributive justice. We propose its application to Nash bargaining theory. The Nash Bargaining Solution (NBS) is characterised by replacing the contriversial Independence of Irrelevant Alternatives axiom with an axiom embodying the Suppes-Sen Principle. More precisely, the Suppes-Sen relation is shown to be equivalent to the (relation implied by the) NBS in the presence of Scale Covariance. The characterisation is far more robust than the standard one with respect to variations in the domain of bargaining problems. It is shown that a subset of Nash's axioms imply the Suppes-Sen relation.

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    Paper provided by EconWPA in its series Game Theory and Information with number 9611003.

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    Length: 27 pages
    Date of creation: 26 Nov 1996
    Date of revision: 27 Nov 1996
    Handle: RePEc:wpa:wuwpga:9611003
    Note: Type of Document - word; prepared on pc; to print on PostScript; pages: 27; figures: included
    Contact details of provider: Web page: http://econwpa.repec.org

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    1. Blackorby, Charles & Bossert, Walter & Donaldson, David, 1994. "Generalized Ginis and Cooperative Bargaining Solutions," Econometrica, Econometric Society, vol. 62(5), pages 1161-78, September.
    2. Herrero, Maria Jose, 1989. "The nash program: Non-convex bargaining problems," Journal of Economic Theory, Elsevier, vol. 49(2), pages 266-277, December.
    3. Shorrocks, Anthony F, 1983. "Ranking Income Distributions," Economica, London School of Economics and Political Science, vol. 50(197), pages 3-17, February.
    4. Kalai, Ehud, 1977. "Proportional Solutions to Bargaining Situations: Interpersonal Utility Comparisons," Econometrica, Econometric Society, vol. 45(7), pages 1623-30, October.
    5. Fernandez, Raquel & Glazer, Jacob, 1991. "Striking for a Bargain between Two Completely Informed Agents," American Economic Review, American Economic Association, vol. 81(1), pages 240-52, March.
    6. Krishna, Vijay & Serrano, Roberto, 1996. "Multilateral Bargaining," Review of Economic Studies, Wiley Blackwell, vol. 63(1), pages 61-80, January.
    7. Nash, John, 1950. "The Bargaining Problem," Econometrica, Econometric Society, vol. 18(2), pages 155-162, April.
    8. Mariotti, Marco, 1994. "The Nash solution and Independence of Revealed Irrelevant Alternatives," Economics Letters, Elsevier, vol. 45(2), pages 175-179, June.
    9. Thomson, A., 1989. "The Consistency Principle," RCER Working Papers 192, University of Rochester - Center for Economic Research (RCER).
    10. Kalai, Ehud & Smorodinsky, Meir, 1975. "Other Solutions to Nash's Bargaining Problem," Econometrica, Econometric Society, vol. 43(3), pages 513-18, May.
    11. Blackorby, Charles & Bossert, Walter & Donaldson, David, 1996. "Consistency, Replication Invariance, and Generalized Gini Bargaining Solutions," Journal of Economic Theory, Elsevier, vol. 69(2), pages 367-386, May.
    12. Haller, Hans & Holden, Steinar, 1990. "A letter to the editor on wage bargaining," Journal of Economic Theory, Elsevier, vol. 52(1), pages 232-236, October.
    13. 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.
    14. John E. ROEMER, 1990. "Welfarism and Axiomatic Bargaining Theory," Discussion Papers (REL - Recherches Economiques de Louvain) 1990032, Université catholique de Louvain, Institut de Recherches Economiques et Sociales (IRES).
    15. repec:cup:cbooks:9780521343831 is not listed on IDEAS
    16. Bossert, Walter, 1994. "Rational choice and two-person bargaining solutions," Journal of Mathematical Economics, Elsevier, vol. 23(6), pages 549-563, November.
    17. Rubinstein, Ariel & Safra, Zvi & Thomson, William, 1992. "On the Interpretation of the Nash Bargaining Solution and Its Extension to Non-expected Utility Preferences," Econometrica, Econometric Society, vol. 60(5), pages 1171-86, September.
    18. Ray, Debraj & Vohra, Rajiv, 1997. "Equilibrium Binding Agreements," Journal of Economic Theory, Elsevier, vol. 73(1), pages 30-78, March.
    19. Blackorby, Charles & Donaldson, David, 1977. "Utility vs equity : Some plausible quasi-orderings," Journal of Public Economics, Elsevier, vol. 7(3), pages 365-381, June.
    20. Myerson, Roger B, 1981. "Utilitarianism, Egalitarianism, and the Timing Effect in Social Choice Problems," Econometrica, Econometric Society, vol. 49(4), pages 883-97, June.
    21. repec:cup:cbooks:9780521027038 is not listed on IDEAS
    22. Conley, John P. & Wilkie, Simon, 1996. "An Extension of the Nash Bargaining Solution to Nonconvex Problems," Games and Economic Behavior, Elsevier, vol. 13(1), pages 26-38, March.
    23. Roth, Alvin E, 1979. "Proportional Solutions to the Bargaining Problem," Econometrica, Econometric Society, vol. 47(3), pages 775-77, May.
    24. Madden, Paul, 1996. "Suppes-Sen dominance, generalised Lorenz dominance and the welfare economics of competitive equilibrium: Some examples," Journal of Public Economics, Elsevier, vol. 61(2), pages 247-262, August.
    25. Ehud Kalai, 1983. "Solutions to the Bargaining Problem," Discussion Papers 556, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    26. Peters, Hans & Wakker, Peter, 1991. "Independence of Irrelevant Alternatives and Revealed Group Preferences," Econometrica, Econometric Society, vol. 59(6), pages 1787-1801, November.
    27. repec:cup:cbooks:9780521424585 is not listed on IDEAS
    28. Alvin E Roth, 2008. "Axiomatic Models of Bargaining," Levine's Working Paper Archive 122247000000002376, David K. Levine.
    29. Lensberg, Terje, 1988. "Stability and the Nash solution," Journal of Economic Theory, Elsevier, vol. 45(2), pages 330-341, August.
    30. Mariotti, Marco, 1997. "A Model of Agreements in Strategic Form Games," Journal of Economic Theory, Elsevier, vol. 74(1), pages 196-217, May.
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