IDEAS home Printed from https://ideas.repec.org/a/jmi/articl/jmi-v6i1a2.html
   My bibliography  Save this article

Axioms concerning uncertain disagreement points in 2-person bargaining problems

Author

Listed:
  • Youngsub Chun

    (Department of Economics, Seoul National University, Korea)

Abstract

We consider 2-person bargaining situations in which the feasible set is known, but the disagreement point is uncertain. We investigate the implications of various axioms concerning uncertain disagreement points and characterize the family of linear solutions, which includes the egalitarian, lexicographic egalitarian, Nash, and Kalai-Rosenthal solutions. We also show that how the important subfamilies (or members) of this family can be singled out by imposing additional axioms or strengthening the axioms used in the characterizations.

Suggested Citation

  • 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.
    • Handle: RePEc:jmi:articl:jmi-v6i1a2
    DOI: 10.22574/jmid.2021.12.002
    as

    Download full text from publisher

    File URL: http://www.mechanism-design.org/arch/v006-1/p_02.pdf
    Download Restriction: no
    File URL: https://libkey.io/10.22574/jmid.2021.12.002?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
    ---><---

    References listed on IDEAS

    as
    1. R.J. Aumann & S. Hart (ed.), 2002. "Handbook of Game Theory with Economic Applications," Handbook of Game Theory with Economic Applications, Elsevier, edition 1, volume 3, number 3.
    2. Thomson,William & Lensberg,Terje, 2006. "Axiomatic Theory of Bargaining with a Variable Number of Agents," Cambridge Books, Cambridge University Press, number 9780521027038.
    3. Chun, Youngsub & Thomson, William, 1990. "Nash solution and uncertain disagreement points," Games and Economic Behavior, Elsevier, vol. 2(3), pages 213-223, September.
    4. Kalai, Ehud, 1977. "Proportional Solutions to Bargaining Situations: Interpersonal Utility Comparisons," Econometrica, Econometric Society, vol. 45(7), pages 1623-1630, October.
    5. Imai, Haruo, 1983. "Individual Monotonicity and Lexicographic Maxmin Solution," Econometrica, Econometric Society, vol. 51(2), pages 389-401, March.
    6. 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.
    7. Nash, John, 1950. "The Bargaining Problem," Econometrica, Econometric Society, vol. 18(2), pages 155-162, April.
    8. Chun, Youngsub, 1990. "Minimal cooperation in bargaining," Economics Letters, Elsevier, vol. 34(4), pages 311-316, December.
    9. Hans Peters & Eric Van Damme, 1991. "Characterizing the Nash and Raiffa Bargaining Solutions by Disagreement Point Axioms," Mathematics of Operations Research, INFORMS, vol. 16(3), pages 447-461, August.
    10. Shiran Rachmilevitch, 2011. "Disagreement point axioms and the egalitarian bargaining solution," International Journal of Game Theory, Springer;Game Theory Society, vol. 40(1), pages 63-85, February.
    11. 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.
    12. Unknown, 1986. "Letters," Choices: The Magazine of Food, Farm, and Resource Issues, Agricultural and Applied Economics Association, vol. 1(4), pages 1-9.
    13. Livne, Zvi, 1986. "The bargaining problem: axioms concerning changes in the conflict point," Economics Letters, Elsevier, vol. 21(2), pages 131-134.
    14. Thomson, William, 1987. "Monotonicity of bargaining solutions with respect to the disagreement point," Journal of Economic Theory, Elsevier, vol. 42(1), pages 50-58, June.
    15. Myerson, Roger B, 1981. "Utilitarianism, Egalitarianism, and the Timing Effect in Social Choice Problems," Econometrica, Econometric Society, vol. 49(4), pages 883-897, June.
    16. Chun, Youngsub, 1988. "Nash solution and timing of bargaining," Economics Letters, Elsevier, vol. 28(1), pages 27-31.
    17. Chun, Youngsub & Thomson, William, 1990. "Egalitarian solutions and uncertain disagreement points," Economics Letters, Elsevier, vol. 33(1), pages 29-33, May.
    18. Anbarci, Nejat & Sun, Ching-jen, 2013. "Robustness of intermediate agreements and bargaining solutions," Games and Economic Behavior, Elsevier, vol. 77(1), pages 367-376.
    19. Zvi A. Livne, 1989. "On the Status Quo Sets Induced by the Raiffa Solution to the Two-Person Bargaining Problem," Mathematics of Operations Research, INFORMS, vol. 14(4), pages 688-692, November.
    20. Chun, Youngsub & Thomson, William, 1990. "Bargaining with Uncertain Disagreement Points," Econometrica, Econometric Society, vol. 58(4), pages 951-959, July.
    21. Peters, Hans J M, 1986. "Simultaneity of Issues and Additivity in Bargaining," Econometrica, Econometric Society, vol. 54(1), pages 153-169, January.
    22. Livne, Zvi A., 1988. "The bargaining problem with an uncertain conflict outcome," Mathematical Social Sciences, Elsevier, vol. 15(3), pages 287-302, June.
    23. Shiran Rachmilevitch, 2011. "A characterization of the Kalai–Smorodinsky bargaining solution by disagreement point monotonicity," International Journal of Game Theory, Springer;Game Theory Society, vol. 40(4), pages 691-696, November.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    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.

    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. Kıbrıs, Özgür & Tapkı, İpek Gürsel, 2011. "Bargaining with nonanonymous disagreement: Decomposable rules," Mathematical Social Sciences, Elsevier, vol. 62(3), pages 151-161.
    2. 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.
    3. 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.
    4. KIbrIs, Özgür & TapkI, Ipek Gürsel, 2010. "Bargaining with nonanonymous disagreement: Monotonic rules," Games and Economic Behavior, Elsevier, vol. 68(1), pages 233-241, January.
    5. Anbarci, Nejat & Sun, Ching-jen, 2013. "Robustness of intermediate agreements and bargaining solutions," Games and Economic Behavior, Elsevier, vol. 77(1), pages 367-376.
    6. 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.
    7. Chun, Youngsub, 2002. "The Converse Consistency Principle in Bargaining," Games and Economic Behavior, Elsevier, vol. 40(1), pages 25-43, July.
    8. Smorodinsky, Rann, 2005. "Nash's bargaining solution when the disagreement point is random," Mathematical Social Sciences, Elsevier, vol. 50(1), pages 3-11, July.
    9. Bas Dietzenbacher & Hans Peters, 2022. "Characterizing NTU-bankruptcy rules using bargaining axioms," Annals of Operations Research, Springer, vol. 318(2), pages 871-888, November.
    10. 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.
    11. Geoffroy Clippel, 2007. "An axiomatization of the Nash bargaining solution," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 29(2), pages 201-210, September.
    12. Chun, Youngsub, 2004. "On weighted Kalai-Samet solutions for non-transferable utility coalitional form games," Games and Economic Behavior, Elsevier, vol. 47(2), pages 257-267, May.
    13. Rachmilevitch, Shiran, "undated". "Gradual Negotiations and Proportional Solutions," Working Papers WP2011/8, University of Haifa, Department of Economics.
    14. Shiran Rachmilevitch, 2022. "Pre-bargaining Investment Implies a Pareto Ranking of Bargaining Solutions," Group Decision and Negotiation, Springer, vol. 31(4), pages 769-787, August.
    15. 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.
    16. Ismail Saglam, 2013. "Endogenously proportional bargaining solutions," Economics Bulletin, AccessEcon, vol. 33(2), pages 1521-1534.
    17. Xu, Yongsheng, 2012. "Symmetry-based compromise and the Nash solution to convex bargaining problems," Economics Letters, Elsevier, vol. 115(3), pages 484-486.
    18. Subrato Banerjee, 2020. "Effect of reduced opportunities on bargaining outcomes: an experiment with status asymmetries," Theory and Decision, Springer, vol. 89(3), pages 313-346, October.
    19. Ismail Saglam, 2014. "A Simple Axiomatization Of The Egalitarian Solution," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 16(04), pages 1-7.
    20. Eyal Winter & Oscar Volij & Nir Dagan, 2002. "A characterization of the Nash bargaining solution," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 19(4), pages 811-823.

    More about this item

    Keywords

    Axiomatic approach to bargaining problems; uncertain disagreement point; linear solutions.;
    All these keywords.

    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
    • D70 - Microeconomics - - Analysis of Collective Decision-Making - - - General

    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:jmi:articl:jmi-v6i1a2. 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: Paul Schweinzer (email available below). General contact details of provider: https://edirc.repec.org/data/deyoruk.html .

    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.