IDEAS home Printed from https://ideas.repec.org/a/spr/sochwe/v62y2024i4d10.1007_s00355-024-01513-6.html
   My bibliography  Save this article

Collective or individual rationality in the Nash bargaining solution: efficiency-free characterizations

Author

Listed:
  • Kensei Nakamura

    (Hitotsubashi University)

Abstract

In the classical bargaining problem, we propose a very mild axiom of individual rationality, which we call possibility of utility gain. This requires that for at least one bargaining problem, there exists at least one player who reaches a higher utility level than their disagreement utility. This paper shows that the Nash solution (Nash in Econometrica 18(2):155–162, 1950) is characterized by possibility of utility gain and continuity with respect to feasible sets together with Nash’s axioms except weak Pareto optimality. We also show that in Nash’s theorem, weak Pareto optimality can be replaced by conflict-freeness (introduced by Rachmilevitch in Math Soc Sci 76(C):107–109, 2015). This demands that when the agreement most preferred by all players is feasible, this should be chosen. Furthermore, we provide alternative and unified proofs for other efficiency-free characterizations of the Nash solution. This clarifies the role of each axiom in the related results.

Suggested Citation

  • Kensei Nakamura, 2024. "Collective or individual rationality in the Nash bargaining solution: efficiency-free characterizations," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 62(4), pages 629-642, June.
  • Handle: RePEc:spr:sochwe:v:62:y:2024:i:4:d:10.1007_s00355-024-01513-6
    DOI: 10.1007/s00355-024-01513-6
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s00355-024-01513-6
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.

    File URL: https://libkey.io/10.1007/s00355-024-01513-6?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Vartiainen, Hannu, 2007. "Collective choice with endogenous reference outcome," Games and Economic Behavior, Elsevier, vol. 58(1), pages 172-180, January.
    2. Chun, Youngsub & Thomson, William, 1990. "Nash solution and uncertain disagreement points," Games and Economic Behavior, Elsevier, vol. 2(3), pages 213-223, September.
    3. Kalai, Ehud, 1977. "Proportional Solutions to Bargaining Situations: Interpersonal Utility Comparisons," Econometrica, Econometric Society, vol. 45(7), pages 1623-1630, October.
    4. Mariotti, Marco, 1996. "Non-optimal Nash Bargaining Solutions," Economics Letters, Elsevier, vol. 52(1), pages 15-20, July.
    5. Shiran Rachmilevitch, 2021. "No individual priorities and the Nash bargaining solution," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 56(4), pages 855-863, May.
    6. Lensberg, T. & Thomson, W., 1988. "Characterizing The Nash Bargaining Solution Without Pareto-Optimality," RCER Working Papers 136, University of Rochester - Center for Economic Research (RCER).
    7. Chun, Youngsub, 1988. "The equal-loss principle for bargaining problems," Economics Letters, Elsevier, vol. 26(2), pages 103-106.
    8. Nejat Anbarci & Ching-jen Sun, 2011. "Weakest collective rationality and the Nash bargaining solution," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 37(3), pages 425-429, September.
    9. Chun, Youngsub & Thomson, William, 1990. "Bargaining with Uncertain Disagreement Points," Econometrica, Econometric Society, vol. 58(4), pages 951-959, July.
    10. van Damme, E.E.C. & Peters, H., 1991. "Characterizing the Nash and Raiffa bargaining solutions by disagreement point axioms," Other publications TiSEM 4bd5eb9e-328a-45a0-aa0a-e, Tilburg University, School of Economics and Management.
    11. 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.
    12. Anbarci, Nejat & Sun, Ching-jen, 2013. "Robustness of intermediate agreements and bargaining solutions," Games and Economic Behavior, Elsevier, vol. 77(1), pages 367-376.
    13. Hans Peters & Walter Bossert, 2002. "Efficient solutions to bargaining problems with uncertain disagreement points," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 19(3), pages 489-502.
    14. Walter Bossert & Hans Peters, 2022. "Individual disagreement point concavity and the bargaining problem," International Journal of Economic Theory, The International Society for Economic Theory, vol. 18(1), pages 6-15, March.
    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. 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.
    2. Youngsub Chun, 2021. "Axioms concerning uncertain disagreement points in 2-person bargaining problems," The Journal of Mechanism and Institution Design, Society for the Promotion of Mechanism and Institution Design, University of York, vol. 6(1), pages 37-58, December.
    3. Dominik Karos & Nozomu Muto & Shiran Rachmilevitch, 2018. "A generalization of the Egalitarian and the Kalai–Smorodinsky bargaining solutions," International Journal of Game Theory, Springer;Game Theory Society, vol. 47(4), pages 1169-1182, November.
    4. Walter Bossert & Hans Peters, 2022. "Individual disagreement point concavity and the bargaining problem," International Journal of Economic Theory, The International Society for Economic Theory, vol. 18(1), pages 6-15, March.
    5. KIbrIs, Özgür & TapkI, Ipek Gürsel, 2010. "Bargaining with nonanonymous disagreement: Monotonic rules," Games and Economic Behavior, Elsevier, vol. 68(1), pages 233-241, January.
    6. Kıbrıs, Özgür & Tapkı, İpek Gürsel, 2011. "Bargaining with nonanonymous disagreement: Decomposable rules," Mathematical Social Sciences, Elsevier, vol. 62(3), pages 151-161.
    7. Smorodinsky, Rann, 2005. "Nash's bargaining solution when the disagreement point is random," Mathematical Social Sciences, Elsevier, vol. 50(1), pages 3-11, July.
    8. NAKAMURA, Kensei, 2023. "Characterizing the Nash bargaining solution with continuity and almost no individual rationality," Discussion Papers 2023-02, Graduate School of Economics, Hitotsubashi University.
    9. Walter Trockel, 2015. "Axiomatization of the discrete Raiffa solution," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 3(1), pages 9-17, April.
    10. Bas Dietzenbacher & Hans Peters, 2022. "Characterizing NTU-bankruptcy rules using bargaining axioms," Annals of Operations Research, Springer, vol. 318(2), pages 871-888, November.
    11. M. Voorneveld & A. Nouweland & R. McLean, 2011. "Axiomatizations of the Euclidean compromise solution," International Journal of Game Theory, Springer;Game Theory Society, vol. 40(3), pages 427-448, August.
    12. Shiran Rachmilevitch, 2021. "Step-by-step negotiations and utilitarianism," International Journal of Game Theory, Springer;Game Theory Society, vol. 50(2), pages 433-445, June.
    13. Shiran Rachmilevitch, 2021. "No individual priorities and the Nash bargaining solution," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 56(4), pages 855-863, May.
    14. Balakrishnan, P.V. (Sundar) & Gómez, Juan Camilo & Vohra, Rakesh V., 2011. "The Tempered Aspirations solution for bargaining problems with a reference point," Mathematical Social Sciences, Elsevier, vol. 62(3), pages 144-150.
    15. Nakamura, Kensei, 2024. "Step-by-step negotiations and the Nash bargaining solution: Efficiency-free characterizations," Economics Letters, Elsevier, vol. 242(C).
    16. Anbarci, Nejat & Sun, Ching-jen, 2013. "Robustness of intermediate agreements and bargaining solutions," Games and Economic Behavior, Elsevier, vol. 77(1), pages 367-376.
    17. Chun, Youngsub, 2002. "The Converse Consistency Principle in Bargaining," Games and Economic Behavior, Elsevier, vol. 40(1), pages 25-43, July.
    18. Rachmilevitch, Shiran, "undated". "Gradual Negotiations and Proportional Solutions," Working Papers WP2011/8, University of Haifa, Department of Economics.
    19. Omer F. Baris, 2018. "Timing effect in bargaining and ex ante efficiency of the relative utilitarian solution," Theory and Decision, Springer, vol. 84(4), pages 547-556, June.
    20. Herrero, Carmen & Maschler, Michael & Villar, Antonio, 1999. "Individual rights and collective responsibility: the rights-egalitarian solution," Mathematical Social Sciences, Elsevier, vol. 37(1), pages 59-77, January.

    More about this item

    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:spr:sochwe:v:62:y:2024:i:4:d:10.1007_s00355-024-01513-6. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.