IDEAS home Printed from https://ideas.repec.org/p/wpa/wuwpga/9611003.html
   My bibliography  Save this paper

Fair bargains: distributive justice and Nash Bargaining Theory

Author

Listed:
  • Marco Mariotii

    (University of Manchester)

Abstract

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.

Suggested Citation

  • Marco Mariotii, 1996. "Fair bargains: distributive justice and Nash Bargaining Theory," Game Theory and Information 9611003, University Library of Munich, Germany, revised 06 Dec 1996.
    • Handle: RePEc:wpa:wuwpga:9611003
    Note: Type of Document - word; prepared on pc; to print on PostScript; pages: 27; figures: included
    as

    Download full text from publisher

    File URL: https://econwpa.ub.uni-muenchen.de/econ-wp/game/papers/9611/9611003.html
    Download Restriction: no
    File URL: https://econwpa.ub.uni-muenchen.de/econ-wp/game/papers/9611/9611003.ps.gz
    Download Restriction: no
    File URL: https://econwpa.ub.uni-muenchen.de/econ-wp/game/papers/9611/9611003.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Thomson,William & Lensberg,Terje, 2006. "Axiomatic Theory of Bargaining with a Variable Number of Agents," Cambridge Books, Cambridge University Press, number 9780521027038.
    2. Kalai, Ehud & Smorodinsky, Meir, 1975. "Other Solutions to Nash's Bargaining Problem," Econometrica, Econometric Society, vol. 43(3), pages 513-518, May.
    3. Peters, Hans & Wakker, Peter, 1991. "Independence of Irrelevant Alternatives and Revealed Group Preferences," Econometrica, Econometric Society, vol. 59(6), pages 1787-1801, November.
    4. Farina, Francesco & Hahn, Frank & Vannucci, Stefano (ed.), 1996. "Ethics, Rationality, and Economic Behaviour," OUP Catalogue, Oxford University Press, number 9780198289814.
    5. Ray, Debraj & Vohra, Rajiv, 1997. "Equilibrium Binding Agreements," Journal of Economic Theory, Elsevier, vol. 73(1), pages 30-78, March.
    6. Kalai, Ehud, 1977. "Proportional Solutions to Bargaining Situations: Interpersonal Utility Comparisons," Econometrica, Econometric Society, vol. 45(7), pages 1623-1630, October.
    7. Bossert, Walter, 1994. "Rational choice and two-person bargaining solutions," Journal of Mathematical Economics, Elsevier, vol. 23(6), pages 549-563, November.
    8. 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).
    9. Nash, John, 1950. "The Bargaining Problem," Econometrica, Econometric Society, vol. 18(2), pages 155-162, April.
    10. Thomson, A., 1989. "The Consistency Principle," RCER Working Papers 192, University of Rochester - Center for Economic Research (RCER).
    11. Roth, Alvin E, 1979. "Proportional Solutions to the Bargaining Problem," Econometrica, Econometric Society, vol. 47(3), pages 775-777, May.
    12. Blackorby, Charles & Donaldson, David, 1977. "Utility vs equity : Some plausible quasi-orderings," Journal of Public Economics, Elsevier, vol. 7(3), pages 365-381, June.
    13. Brams,Steven J. & Taylor,Alan D., 1996. "Fair Division," Cambridge Books, Cambridge University Press, number 9780521556446.
    14. Ehud Kalai, 1983. "Solutions to the Bargaining Problem," Discussion Papers 556, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    15. Mariotti, Marco, 1997. "A Model of Agreements in Strategic Form Games," Journal of Economic Theory, Elsevier, vol. 74(1), pages 196-217, May.
    16. Blackorby, Charles & Bossert, Walter & Donaldson, David, 1994. "Generalized Ginis and Cooperative Bargaining Solutions," Econometrica, Econometric Society, vol. 62(5), pages 1161-1178, September.
    17. Fernandez, Raquel & Glazer, Jacob, 1991. "Striking for a Bargain between Two Completely Informed Agents," American Economic Review, American Economic Association, vol. 81(1), pages 240-252, March.
    18. Herrero, Maria Jose, 1989. "The nash program: Non-convex bargaining problems," Journal of Economic Theory, Elsevier, vol. 49(2), pages 266-277, December.
    19. 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 1171-1186, September.
    20. Mariotti, Marco, 1994. "The Nash solution and Independence of Revealed Irrelevant Alternatives," Economics Letters, Elsevier, vol. 45(2), pages 175-179, June.
    21. 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.
    22. Shorrocks, Anthony F, 1983. "Ranking Income Distributions," Economica, London School of Economics and Political Science, vol. 50(197), pages 3-17, February.
    23. Myerson, Roger B, 1981. "Utilitarianism, Egalitarianism, and the Timing Effect in Social Choice Problems," Econometrica, Econometric Society, vol. 49(4), pages 883-897, June.
    24. 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.
    25. 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.
    26. 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.
    27. Alvin E Roth, 2008. "Axiomatic Models of Bargaining," Levine's Working Paper Archive 122247000000002376, David K. Levine.
    28. Rubin Saposnik, 1983. "On evaluating income distributions: Rank dominance, the Suppes-Sen grading principle of justice, and Pareto optimality," Public Choice, Springer, vol. 40(3), pages 329-336, January.
    29. 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.
    30. Lensberg, Terje, 1988. "Stability and the Nash solution," Journal of Economic Theory, Elsevier, vol. 45(2), pages 330-341, August.
    31. Vijay Krishna & Roberto Serrano, 1996. "Multilateral Bargaining," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 63(1), pages 61-80.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Ok, Efe A., 1998. "Inequality averse collective choice," Journal of Mathematical Economics, Elsevier, vol. 30(3), pages 301-321, October.
    2. Yongsheng Xu & Naoki Yoshihara, 2020. "Nonconvex Bargaining Problems: Some Recent Developments," Homo Oeconomicus: Journal of Behavioral and Institutional Economics, Springer, vol. 37(1), pages 7-41, November.
    3. Ok, Efe A. & Zhou, Lin, 2000. "The Choquet Bargaining Solutions," Games and Economic Behavior, Elsevier, vol. 33(2), pages 249-264, November.
    4. Driesen, Bram, 2016. "Truncated Leximin solutions," Mathematical Social Sciences, Elsevier, vol. 83(C), pages 79-87.
    5. Serrano, Roberto & Shimomura, Ken-Ichi, 1998. "Beyond Nash Bargaining Theory: The Nash Set," Journal of Economic Theory, Elsevier, vol. 83(2), pages 286-307, December.
    6. William Thomson, 2022. "On the axiomatic theory of bargaining: a survey of recent results," Review of Economic Design, Springer;Society for Economic Design, vol. 26(4), pages 491-542, December.
    7. Roberto Serrano, 2005. "Fifty years of the Nash program, 1953-2003," Investigaciones Economicas, Fundación SEPI, vol. 29(2), pages 219-258, May.
    8. Roberto Serrano, 2004. "Fifty Years of the Nash Program, 1953-2003," Working Papers 2004-20, Brown University, Department of Economics.
    9. David H. Wolpert & James Bono, 2010. "A theory of unstructured bargaining using distribution-valued solution concepts," Working Papers 2010-14, American University, Department of Economics.
    10. Ismail Saglam, 2013. "Endogenously proportional bargaining solutions," Economics Bulletin, AccessEcon, vol. 33(2), pages 1521-1534.
    11. Roberto Serrano, 2007. "Bargaining," Working Papers 2007-06, Instituto Madrileño de Estudios Avanzados (IMDEA) Ciencias Sociales.
    12. Youngsub Chun, 2001. "The Separability Principle in Bargaining," Working Paper Series no43, Institute of Economic Research, Seoul National University.
    13. Zapechelnyuk, Andriy, 2013. "Eliciting information from a committee," Journal of Economic Theory, Elsevier, vol. 148(5), pages 2049-2067.
    14. Cheng-Zhong Qin & Shuzhong Shi & Guofu Tan, 2015. "Nash bargaining for log-convex problems," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 58(3), pages 413-440, April.
    15. Rebelo, S., 1997. "On the Determinant of Economic Growth," RCER Working Papers 443, University of Rochester - Center for Economic Research (RCER).
    16. Yongsheng Xu & Naoki Yoshihara, 2019. "An equitable Nash solution to nonconvex bargaining problems," International Journal of Game Theory, Springer;Game Theory Society, vol. 48(3), pages 769-779, September.
    17. Chun, Youngsub, 2002. "The Converse Consistency Principle in Bargaining," Games and Economic Behavior, Elsevier, vol. 40(1), pages 25-43, July.
    18. Nejat Anbarci, 2008. "Relative Responsiveness of Bargaining Solutions to Changes in Status-quo Payoffs," Atlantic Economic Journal, Springer;International Atlantic Economic Society, vol. 36(3), pages 293-299, September.
    19. Jerry Green, 2005. "Compensatory transfers in two-player decision problems," International Journal of Game Theory, Springer;Game Theory Society, vol. 33(2), pages 159-180, June.
    20. 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.

    More about this item

    Keywords

    Suppes-Sen NBS;

    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
    • C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:wpa:wuwpga:9611003. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: EconWPA (email available below). General contact details of provider: https://econwpa.ub.uni-muenchen.de .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.