IDEAS home Printed from https://ideas.repec.org/p/pab/wpaper/07.13.html
   My bibliography  Save this paper

Multi-Utilitarian Bargaining Solutions

Author

Listed:
  • Miguel Ángel Hinojosa

    (Department of Economics, Quantitative Methods and Economic History, Universidad Pablo de Olavide)

  • Amparo Mª Mármol

    (Department of Applied Economics III, Universidad de Sevilla)

  • José Manuel Zarzuelo

    (Department of Applied Economics IV, Universidad del País Vasco)

Abstract

This paper introduces and analyzes the class of multi-utilitarian solutions for cooperative bargaining problems. We show that generalized Gini solutions and inequality averse Choquet bargaining solutions are particular cases of this new multi-valued solution concept and provide a complete characterization of inequality averse multi-utilitarian solutions in which an invariance property consisting of a weakening of both the linear invariance axiom in Blackorby et al. (1994) and the restricted invariance axiom in Ok and Zhou (2000). Moreover, by relaxing the assumptions involved in the characterization, the class is extended to include equality averse multi-utilitarian solutions which are also studied in the paper.

Suggested Citation

  • Miguel Ángel Hinojosa & Amparo Mª Mármol & José Manuel Zarzuelo, 2007. "Multi-Utilitarian Bargaining Solutions," Working Papers 07.13, Universidad Pablo de Olavide, Department of Economics.
    • Handle: RePEc:pab:wpaper:07.13
    as

    Download full text from publisher

    File URL: http://www.upo.es/serv/bib/wps/econ0713.pdf
    File Function: First version, 2007
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Ok, Efe A. & Zhou, Lin, 2000. "The Choquet Bargaining Solutions," Games and Economic Behavior, Elsevier, vol. 33(2), pages 249-264, November.
    2. Kalai, Ehud, 1977. "Proportional Solutions to Bargaining Situations: Interpersonal Utility Comparisons," Econometrica, Econometric Society, vol. 45(7), pages 1623-1630, October.
    3. Efe A. Ok & Lin Zhou, 1999. "Revealed group preferences on non-convex choice problems," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 13(3), pages 671-687.
    4. Nash, John, 1950. "The Bargaining Problem," Econometrica, Econometric Society, vol. 18(2), pages 155-162, April.
    5. Myerson, Roger B, 1977. "Two-Person Bargaining Problems and Comparable Utility," Econometrica, Econometric Society, vol. 45(7), pages 1631-1637, October.
    6. Blackorby, Charles & Bossert, Walter & Donaldson, David, 1994. "Generalized Ginis and Cooperative Bargaining Solutions," Econometrica, Econometric Society, vol. 62(5), pages 1161-1178, September.
    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. M. Hinojosa & A. Mármol & J. Zarzuelo, 2008. "Inequality averse multi-utilitarian bargaining solutions," International Journal of Game Theory, Springer;Game Theory Society, vol. 37(4), pages 597-618, December.
    2. Ok, Efe A. & Zhou, Lin, 2000. "The Choquet Bargaining Solutions," Games and Economic Behavior, Elsevier, vol. 33(2), pages 249-264, November.
    3. Ok, Efe A., 1998. "Inequality averse collective choice," Journal of Mathematical Economics, Elsevier, vol. 30(3), pages 301-321, October.
    4. Eric van Damme & Xu Lang, 2022. "Two-Person Bargaining when the Disagreement Point is Private Information," Papers 2211.06830, arXiv.org, revised Jan 2024.
    5. 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.
    6. 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.
    7. 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.
    8. Eric van Damme, 1984. "The Nash Bargaining Solution is Optimal," Discussion Papers 597, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    9. Barry Feldman, 2005. "Lost in Translation? Basis Utility and Proportionality in Games," Game Theory and Information 0507001, University Library of Munich, Germany, revised 28 Feb 2006.
    10. Navarro, Noemí & Veszteg, Róbert F., 2020. "On the empirical validity of axioms in unstructured bargaining," Games and Economic Behavior, Elsevier, vol. 121(C), pages 117-145.
    11. M. Carmen Marco & Josep E. Peris & Begoña Subiza, 2020. "A Concessions-Based Procedure for Meta-Bargaining Problems," Homo Oeconomicus: Journal of Behavioral and Institutional Economics, Springer, vol. 37(1), pages 105-120, November.
    12. Salonen, Hannu, 1998. "Egalitarian solutions for n-person bargaining games," Mathematical Social Sciences, Elsevier, vol. 35(3), pages 291-306, May.
    13. Ehud Kalai, 1983. "Solutions to the Bargaining Problem," Discussion Papers 556, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    14. Kibris, Ozgur, 2004. "Egalitarianism in ordinal bargaining: the Shapley-Shubik rule," Games and Economic Behavior, Elsevier, vol. 49(1), pages 157-170, October.
    15. Marco-Gil, Maria del Carmen & Peris, Josep E. & Subiza, Begoña, 2012. "A Concessions-Based Mechanism for Meta-Bargaining Problems," QM&ET Working Papers 12-13, University of Alicante, D. Quantitative Methods and Economic Theory.
    16. Zvi A. Livne, 1981. "An Extension of the Nash Bargaining Problem: Introducing Time-Related Bargaining Costs," Cowles Foundation Discussion Papers 550, Cowles Foundation for Research in Economics, Yale University.
    17. Bergantiños, Gustavo & Moreno-Ternero, Juan D., 2022. "Monotonicity in sharing the revenues from broadcasting sports leagues," European Journal of Operational Research, Elsevier, vol. 297(1), pages 338-346.
    18. Yoshihara, Naoki, 2003. "Characterizations of bargaining solutions in production economies with unequal skills," Journal of Economic Theory, Elsevier, vol. 108(2), pages 256-285, February.
    19. Juarez, Ruben & Ko, Chiu Yu & Xue, Jingyi, 2018. "Sharing sequential values in a network," Journal of Economic Theory, Elsevier, vol. 177(C), pages 734-779.
    20. Radzvilas, Mantas, 2016. "Hypothetical Bargaining and the Equilibrium Selection Problem in Non-Cooperative Games," MPRA Paper 70248, University Library of Munich, Germany.

    More about this item

    Keywords

    Axiomatic bargaining theory; multi-valued bargaining solutions; generalized Gini solutions; inequality adverse Choquet solutions.;
    All these keywords.

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory

    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:pab:wpaper:07.13. 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: Publicación Digital - UPO (email available below). General contact details of provider: https://edirc.repec.org/data/deupoes.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.