IDEAS home Printed from https://ideas.repec.org/a/eee/gamebe/v142y2023icp730-742.html
   My bibliography  Save this article

Bargaining: Nash, Consensus, or Compromise?

Author

Listed:
  • Li, Xiangliang

Abstract

We propose two solutions to Nash (1950)'s bargaining problem: the Consensus and Compromise solutions. They gradually diverge from the Nash solution. Regarding axioms, we decompose the Nash solution's Axiom IIA (Independence of Irrelevant Alternatives) into distinct parts. The controversial ones are identified and successively replaced, leading to the Consensus and Compromise solutions. The two replacement parts are: 1). If the additional room for cooperation, resulting from deteriorating non-cooperation, does not offer a better outcome for both players, the solution remains unchanged; 2). A solution should not be the best only for one player, i.e., each player should make at least some concession, no matter how small.

Suggested Citation

  • Li, Xiangliang, 2023. "Bargaining: Nash, Consensus, or Compromise?," Games and Economic Behavior, Elsevier, vol. 142(C), pages 730-742.
    • Handle: RePEc:eee:gamebe:v:142:y:2023:i:c:p:730-742
    DOI: 10.1016/j.geb.2023.09.011
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0899825623001483
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.geb.2023.09.011?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. Anbarci, Nejat & Bigelow, John P., 1994. "The area monotonic solution to the cooperative bargaining problem," Mathematical Social Sciences, Elsevier, vol. 28(2), pages 133-142, October.
    2. Christopher A. Pissarides, 2000. "Equilibrium Unemployment Theory, 2nd Edition," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262161877, December.
    3. Jean Tirole, 1988. "The Theory of Industrial Organization," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262200716, December.
    4. Grossman, Sanford J & Hart, Oliver D, 1986. "The Costs and Benefits of Ownership: A Theory of Vertical and Lateral Integration," Journal of Political Economy, University of Chicago Press, vol. 94(4), pages 691-719, August.
    5. Chiappori, Pierre-Andre, 1992. "Collective Labor Supply and Welfare," Journal of Political Economy, University of Chicago Press, vol. 100(3), pages 437-467, June.
    6. Andrei Shleifer & Robert W. Vishny, 1994. "Politicians and Firms," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 109(4), pages 995-1025.
    7. 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.
    8. Kalai, Ehud & Smorodinsky, Meir, 1975. "Other Solutions to Nash's Bargaining Problem," Econometrica, Econometric Society, vol. 43(3), pages 513-518, May.
    9. Imai, Haruo, 1983. "Individual Monotonicity and Lexicographic Maxmin Solution," Econometrica, Econometric Society, vol. 51(2), pages 389-401, March.
    10. Zvi A. Livne, 1989. "Axiomatic Characterizations of the Raiffa and the Kalai-Smorodinsky Solutions to the Bargaining Problem," Operations Research, INFORMS, vol. 37(6), pages 972-980, December.
    11. Manser, Marilyn & Brown, Murray, 1980. "Marriage and Household Decision-Making: A Bargaining Analysis," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 21(1), pages 31-44, February.
    12. 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.
    13. 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.
    14. Hart, Oliver, 1995. "Firms, Contracts, and Financial Structure," OUP Catalogue, Oxford University Press, number 9780198288817.
    15. Kreps, David M., 1990. "Game Theory and Economic Modelling," OUP Catalogue, Oxford University Press, number 9780198283812.
    16. Partha Dasgupta & Eric S. Maskin, 2007. "Bargaining and Destructive Power," Annals of Economics and Finance, Society for AEF, vol. 8(2), pages 217-227, November.
    17. McElroy, Marjorie B & Horney, Mary Jean, 1981. "Nash-Bargained Household Decisions: Toward a Generalization of the Theory of Demand," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 22(2), pages 333-349, June.
    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. Mehrdad Vahabi, 1999. "From Walrasian General Equilibrium to Incomplete Contracts: Making Sense of Institutions," Post-Print halshs-03704424, HAL.
    2. Francesconi, Marco & Muthoo, Abhinay, 2003. "An Economic Model of Child Custody," IZA Discussion Papers 857, Institute of Labor Economics (IZA).
    3. Matthew J. Baker & Joyce P. Jacobsen, 2007. "Marriage, Specialization, and the Gender Division of Labor," Journal of Labor Economics, University of Chicago Press, vol. 25(4), pages 763-793.
    4. 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.
    5. l'Haridon, Olivier & Malherbet, Franck & Pérez-Duarte, Sébastien, 2013. "Does bargaining matter in the small firms matching model?," Labour Economics, Elsevier, vol. 21(C), pages 42-58.
    6. Pierre-André Chiappori & Olivier Donni, 2005. "Learning From a Piece of Pie: The Empirical Content of Nash Bargaining," THEMA Working Papers 2006-07, THEMA (THéorie Economique, Modélisation et Applications), Université de Cergy-Pontoise.
    7. Laurens Cherchye & Thomas Demuynck & Bram De Rock, 2013. "Nash‐Bargained Consumption Decisions: A Revealed Preference Analysis," Economic Journal, Royal Economic Society, vol. 123, pages 195-235, March.
    8. 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.
    9. 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.
    10. 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.
    11. Robert A. Pollak, 2005. "Bargaining Power in Marriage: Earnings, Wage Rates and Household Production," NBER Working Papers 11239, National Bureau of Economic Research, Inc.
    12. Carvajal, Andrés & González, Natalia, 2014. "On refutability of the Nash bargaining solution," Journal of Mathematical Economics, Elsevier, vol. 50(C), pages 177-186.
    13. Ephraim Zehavi & Amir Leshem, 2018. "On the Allocation of Multiple Divisible Assets to Players with Different Utilities," Computational Economics, Springer;Society for Computational Economics, vol. 52(1), pages 253-274, June.
    14. Patricia Apps & Ray Rees, 2007. "Household Models: An Historical Perspective," CESifo Working Paper Series 2172, CESifo.
    15. Blau, David M. & Riphahn, Regina T., 1999. "Labor force transitions of older married couples in Germany," Labour Economics, Elsevier, vol. 6(2), pages 229-252, June.
    16. Asiedu, Elizabeth & Azomahou, Théophile T. & Getachew, Yoseph & Yitbarek, Eleni, 2021. "Share the love: Parental bias, women empowerment and intergenerational mobility," Journal of Economic Behavior & Organization, Elsevier, vol. 191(C), pages 846-867.
    17. Jara-Díaz, Sergio & Rosales-Salas, Jorge, 2017. "Beyond transport time: A review of time use modeling," Transportation Research Part A: Policy and Practice, Elsevier, vol. 97(C), pages 209-230.
    18. repec:hal:spmain:info:hdl:2441/5j2m1g6i7j8pnapkjvifl6e30f is not listed on IDEAS
    19. Alberto Alesina & Andrea Ichino & Loukas Karabarbounis, 2011. "Gender-Based Taxation and the Division of Family Chores," American Economic Journal: Economic Policy, American Economic Association, vol. 3(2), pages 1-40, May.
    20. Gustman, Alan L & Steinmeier, Thomas L, 2000. "Retirement in Dual-Career Families: A Structural Model," Journal of Labor Economics, University of Chicago Press, vol. 18(3), pages 503-545, July.
    21. Schmitz, Patrick W., 2013. "Job design with conflicting tasks reconsidered," European Economic Review, Elsevier, vol. 57(C), pages 108-117.

    More about this item

    Keywords

    Bargaining; Nash solution; Consensus; Compromise; No-cooperation; Cooperation;
    All these keywords.

    JEL classification:

    • D01 - Microeconomics - - General - - - Microeconomic Behavior: Underlying Principles
    • C70 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - General
    • 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:eee:gamebe:v:142:y:2023:i:c:p:730-742. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/inca/622836 .

    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.