IDEAS home Printed from https://ideas.repec.org/p/vnm/wpdman/150.html
   My bibliography  Save this paper

The probability to reach an agreement as a foundation for axiomatic bargaining

Author

Listed:
  • Lorenzo Bastianello

    (LEMMA Universite Paris 2 Pantheon-Assas)

  • Marco LiCalzi

    (Dept. of Management, Università Ca' Foscari Venice)

Abstract

We revisit the Nash bargaining model and axiomatize a procedural solution that maximizes the probability of successful bargaining. This probability-based approach nests both the standard and the ordinal Nash solution, and yet need not assume that bargainers have preferences over lotteries or that choice sets are convex. We consider both mediator-assisted bargaining and standard unassisted bargaining. We solve a long-standing puzzle and offer a natural interpretation of the product operator underlying the Nash solution. We characterize other known solution concepts, including the egalitarian and the utilitarian solutions.

Suggested Citation

  • Lorenzo Bastianello & Marco LiCalzi, 2018. "The probability to reach an agreement as a foundation for axiomatic bargaining," Working Papers 02, Venice School of Management - Department of Management, Università Ca' Foscari Venezia.
    • Handle: RePEc:vnm:wpdman:150
    as

    Download full text from publisher

    File URL: https://www.unive.it/web/fileadmin/user_upload/dipartimenti/DMAN/pubblicazioni_scientifiche/working_papers/2018/2018wp02.pdf
    File Function: First version, 2018
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Kalai, Ehud, 1977. "Proportional Solutions to Bargaining Situations: Interpersonal Utility Comparisons," Econometrica, Econometric Society, vol. 45(7), pages 1623-1630, October.
    2. 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.
    3. Marco LiCalzi, 2005. "A language for the construction of preferences under uncertainty," Game Theory and Information 0509002, University Library of Munich, Germany.
    4. Erio Castagnoli & Marco LiCalzi, 2005. "Expected utility without utility," Game Theory and Information 0508004, University Library of Munich, Germany.
    5. 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.
    6. Trockel, W., 2008. "The Nash product is a utility representation of the Pareto ordering," Economics Letters, Elsevier, vol. 99(2), pages 220-222, May.
    7. John C. Harsanyi & Reinhard Selten, 1972. "A Generalized Nash Solution for Two-Person Bargaining Games with Incomplete Information," Management Science, INFORMS, vol. 18(5-Part-2), pages 80-106, January.
    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. Harstad, Bård, 2023. "Pledge-and-review bargaining," Journal of Economic Theory, Elsevier, vol. 207(C).
    2. 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.
    3. Harstad, Bård, 2021. "A Theory of Pledge-and-Review Bargaining," Memorandum 5/2022, Oslo University, Department of Economics, revised 21 Jun 2021.
    4. Luis C. Dias & Rudolf Vetschera, 2022. "Two-party Bargaining Processes Based on Subjective Expectations: A Model and a Simulation Study," Group Decision and Negotiation, Springer, vol. 31(4), pages 843-869, August.
    5. Yoshio Kamijo, 2023. "Fixation of inequality and emergence of the equal split norm: Approach from behavioral bargaining theory," Working Papers 2209, Waseda University, Faculty of Political Science and Economics, revised Jun 2023.

    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. Lorenzo Bastianello & Marco LiCalzi, 2015. "Target-based solutions for Nash bargaining," Working Papers 5, Venice School of Management - Department of Management, Università Ca' Foscari Venezia.
    2. José-Manuel Giménez-Gómez & António Osório & Josep E. Peris, 2015. "From Bargaining Solutions to Claims Rules: A Proportional Approach," Games, MDPI, vol. 6(1), pages 1-7, March.
    3. Forgo, F. & Szidarovszky, F., 2003. "On the relation between the Nash bargaining solution and the weighting method," European Journal of Operational Research, Elsevier, vol. 147(1), pages 108-116, May.
    4. Özgür Kıbrıs & Murat Sertel, 2007. "Bargaining over a finite set of alternatives," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 28(3), pages 421-437, April.
    5. Joan Esteban & Jozsef Sakovics, 1999. "Why do lions get the lion's share? A Hobbesian theory of agreements," Edinburgh School of Economics Discussion Paper Series 37, Edinburgh School of Economics, University of Edinburgh.
    6. Eric van Damme & Xu Lang, 2022. "Two-Person Bargaining when the Disagreement Point is Private Information," Papers 2211.06830, arXiv.org, revised Jan 2024.
    7. Jaume García Segarra & Miguel Ginés Vilar, 2011. "Weighted Proportional Losses Solution," ThE Papers 10/21, Department of Economic Theory and Economic History of the University of Granada..
    8. Ismail Saglam, 2013. "Endogenously proportional bargaining solutions," Economics Bulletin, AccessEcon, vol. 33(2), pages 1521-1534.
    9. Guillaume Rocheteau & Randall Wright & Cathy Zhang, 2018. "Corporate Finance and Monetary Policy," American Economic Review, American Economic Association, vol. 108(4-5), pages 1147-1186, April.
    10. Huber, Samuel & Kim, Jaehong, 2019. "The role of trading frictions in financial markets," Journal of Economic Dynamics and Control, Elsevier, vol. 99(C), pages 1-18.
    11. Robert Bordley & Marco Licalzi & Luisa Tibiletti, 2017. "A Target-Based Foundation for the “Hard-Easy Effect” Bias," Eurasian Studies in Business and Economics, in: Mehmet Huseyin Bilgin & Hakan Danis & Ender Demir & Ugur Can (ed.), Country Experiences in Economic Development, Management and Entrepreneurship, pages 659-671, Springer.
    12. Lombardi, Michele & Yoshihara, Naoki, 2010. "Alternative characterizations of the proportional solution for nonconvex bargaining problems with claims," Economics Letters, Elsevier, vol. 108(2), pages 229-232, August.
    13. Ronghuo Zheng & Tinglong Dai & Katia Sycara & Nilanjan Chakraborty, 2016. "Automated Multilateral Negotiation on Multiple Issues with Private Information," INFORMS Journal on Computing, INFORMS, vol. 28(4), pages 612-628, November.
    14. Nicolo, Antonio & Perea, Andres, 2005. "Monotonicity and equal-opportunity equivalence in bargaining," Mathematical Social Sciences, Elsevier, vol. 49(2), pages 221-243, March.
    15. Safra, Zvi & Samet, Dov, 2004. "An ordinal solution to bargaining problems with many players," Games and Economic Behavior, Elsevier, vol. 46(1), pages 129-142, January.
    16. Claus-Jochen Haake & Cheng-Zhong Qin, 2018. "On unification of solutions to the bargaining problem," Working Papers CIE 113, Paderborn University, CIE Center for International Economics.
    17. Youngsub Chun, 2001. "The Separability Principle in Bargaining," Working Paper Series no43, Institute of Economic Research, Seoul National University.
    18. Sergiy Gerasymchuk, 2007. "Mean-Variance Portfolio Selection with Reference Dependent Preferences," Working Papers 150, Department of Applied Mathematics, Università Ca' Foscari Venezia.
    19. 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.
    20. S. Nuray Akin & Murat R. Sertel, 2007. "The Kalai-Smorodinsky Bargaining Solution Manipulated by Pre-Donations is Concessionary," Working Papers 0718, University of Miami, Department of Economics.

    More about this item

    Keywords

    cooperative bargaining; mediation; arbitration; benchmarking; copulas.;
    All these keywords.

    JEL classification:

    • C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory
    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
    • D74 - Microeconomics - - Analysis of Collective Decision-Making - - - Conflict; Conflict Resolution; Alliances; Revolutions

    NEP fields

    This paper has been announced in the following NEP Reports:

    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:vnm:wpdman:150. 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: Daria Arkhipova (email available below). General contact details of provider: https://edirc.repec.org/data/mdvenit.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.