IDEAS home Printed from https://ideas.repec.org/a/eee/matsoc/v83y2016icp79-87.html
   My bibliography  Save this article

Truncated Leximin solutions

Author

Listed:
  • Driesen, Bram

Abstract

This paper shows that three classic properties for bargaining solutions in an environment with a variable number of agents–Anonymity (AN), Individual Monotonicity (IM), and Consistency (CONS)–characterize a one-parameter family of Truncated Leximin solutions. Given a non-negative and possibly infinite α, an α-Truncated Leximin solution gives each agent the minimum of α and their Leximin solution payoff.

Suggested Citation

  • Driesen, Bram, 2016. "Truncated Leximin solutions," Mathematical Social Sciences, Elsevier, vol. 83(C), pages 79-87.
    • Handle: RePEc:eee:matsoc:v:83:y:2016:i:c:p:79-87
    DOI: 10.1016/j.mathsocsci.2016.07.003
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0165489616300543
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.mathsocsci.2016.07.003?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. Alvin E. Roth, 1977. "Individual Rationality and Nash's Solution to the Bargaining Problem," Mathematics of Operations Research, INFORMS, vol. 2(1), pages 64-65, February.
    2. Thomson,William & Lensberg,Terje, 2006. "Axiomatic Theory of Bargaining with a Variable Number of Agents," Cambridge Books, Cambridge University Press, number 9780521027038, January.
    3. Kalai, Ehud & Smorodinsky, Meir, 1975. "Other Solutions to Nash's Bargaining Problem," Econometrica, Econometric Society, vol. 43(3), pages 513-518, May.
    4. Kalai, Ehud, 1977. "Proportional Solutions to Bargaining Situations: Interpersonal Utility Comparisons," Econometrica, Econometric Society, vol. 45(7), pages 1623-1630, October.
    5. Mark A. Chen, 2000. "Individual monotonicity and the leximin solution," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 15(2), pages 353-365.
    6. Imai, Haruo, 1983. "Individual Monotonicity and Lexicographic Maxmin Solution," Econometrica, Econometric Society, vol. 51(2), pages 389-401, March.
    7. Thomson, William, 1980. "Two characterizations of the Raiffa solution," Economics Letters, Elsevier, vol. 6(3), pages 225-231.
    8. Nash, John, 1950. "The Bargaining Problem," Econometrica, Econometric Society, vol. 18(2), pages 155-162, April.
    9. Hammond, Peter J, 1976. "Equity, Arrow's Conditions, and Rawls' Difference Principle," Econometrica, Econometric Society, vol. 44(4), pages 793-804, July.
    10. Thomson, William, 1983. "Problems of fair division and the Egalitarian solution," Journal of Economic Theory, Elsevier, vol. 31(2), pages 211-226, December.
    11. Roth, Alvin E, 1979. "Proportional Solutions to the Bargaining Problem," Econometrica, Econometric Society, vol. 47(3), pages 775-777, May.
    12. William Thomson (ed.), 2010. "Bargaining and the Theory of Cooperative Games: John Nash and Beyond," Books, Edward Elgar Publishing, number 13317.
    13. 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).
    14. Li, Duozhe, 2007. "Bargaining with history-dependent preferences," Journal of Economic Theory, Elsevier, vol. 136(1), pages 695-708, September.
    15. Lensberg, Terje, 1988. "Stability and the Nash solution," Journal of Economic Theory, Elsevier, vol. 45(2), pages 330-341, August.
    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. Jaume García-Segarra & Miguel Ginés-Vilar, 2019. "Stagnation proofness in n-agent bargaining problems," Journal of Economic Interaction and Coordination, Springer;Society for Economic Science with Heterogeneous Interacting Agents, vol. 14(1), pages 215-224, March.
    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. 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.

    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. Bram Driesen, 2016. "Bargaining, conditional consistency, and weighted lexicographic Kalai-Smorodinsky Solutions," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 46(4), pages 777-809, April.
    2. William Thomson, 2020. "Reconciling Consistency and Continuity: A Bounded-Population Characterization of the Nash Bargaining Solution," Homo Oeconomicus: Journal of Behavioral and Institutional Economics, Springer, vol. 37(1), pages 43-57, November.
    3. 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.
    4. 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.
    5. Driesen, Bram, 2012. "Proportional concessions and the leximin solution," Economics Letters, Elsevier, vol. 114(3), pages 288-291.
    6. Youngsub Chun, 2001. "The Replacement Principle in Bargaining," Working Paper Series no42, Institute of Economic Research, Seoul National University.
    7. Kaminski, Marek M., 2004. "Social choice and information: the informational structure of uniqueness theorems in axiomatic social theories," Mathematical Social Sciences, Elsevier, vol. 48(2), pages 121-138, September.
    8. Youngsub Chun, 2020. "Some Impossibility Results on the Converse Consistency Principle in Bargaining," Homo Oeconomicus: Journal of Behavioral and Institutional Economics, Springer, vol. 37(1), pages 59-65, November.
    9. Rachmilevitch, Shiran, 2015. "Nash bargaining with (almost) no rationality," Mathematical Social Sciences, Elsevier, vol. 76(C), pages 107-109.
    10. 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.
    11. Youngsub Chun, 2001. "The Separability Principle in Bargaining," Working Paper Series no43, Institute of Economic Research, Seoul National University.
    12. Albizuri, M.J. & Dietzenbacher, B.J. & Zarzuelo, J.M., 2020. "Bargaining with independence of higher or irrelevant claims," Journal of Mathematical Economics, Elsevier, vol. 91(C), pages 11-17.
    13. Rebelo, S., 1997. "On the Determinant of Economic Growth," RCER Working Papers 443, University of Rochester - Center for Economic Research (RCER).
    14. Chun, Youngsub, 2002. "The Converse Consistency Principle in Bargaining," Games and Economic Behavior, Elsevier, vol. 40(1), pages 25-43, July.
    15. I. Contreras & S. Lozano & M. A. Hinojosa, 2021. "A bargaining approach to determine common weights in DEA," Operational Research, Springer, vol. 21(3), pages 2181-2201, September.
    16. 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.
    17. 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.
    18. 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.
    19. 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.
    20. Ismail Saglam, 2017. "Iterated Kalai–Smorodinsky–Nash compromise," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 40(1), pages 335-349, November.

    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:eee:matsoc:v:83:y:2016:i:c:p:79-87. 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/505565 .

    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.