IDEAS home Printed from https://ideas.repec.org/p/awi/wpaper/0523.html
   My bibliography  Save this paper

The Asymmetric Leximin Solution

Author

Listed:
  • Driesen, Bram W.

Abstract

In this article we define and characterize a class of asymmetric leximin solutions, that contains both the symmetric leximin solution of Imai[5] and the two-person asymmetric Kalai-Smorodinsky solution of Dubra [3] as special cases. Solutions in this class combine three attractive features: they are defined on the entire domain of convex n-person bargaining problems, they generally yield Pareto efficient solution outcomes, and asymmetries among bargainers are captured by a single parameter vector. The characterization is based on a strengthening of Dubra’s [3] property Restricted Independence of Irrelevant Alternatives (RIIA). RIIA imposes Nash’s IIA (Nash [9]), under the added condition that the contraction of the feasible set preserves the mutual proportions of players’ utopia values. Our axiom, entitled RIIA for Independent Players (RIP), says RIIA holds for a group of players, given that the contraction of the feasible set does not affect players outside that group.

Suggested Citation

  • Driesen, Bram W., 2012. "The Asymmetric Leximin Solution," Working Papers 0523, University of Heidelberg, Department of Economics.
    • Handle: RePEc:awi:wpaper:0523
    Note: This paper is part of http://archiv.ub.uni-heidelberg.de/volltextserver/view/schriftenreihen/sr-3.html
    as

    Download full text from publisher

    File URL: http://nbn-resolving.de/urn/resolver.pl?urn=urn:nbn:de:bsz:16-opus-131244
    File Function: Frontdoor page on HeiDOK
    Download Restriction: no
    File URL: https://archiv.ub.uni-heidelberg.de/volltextserver/13124/1/Driesen_2012_dp523_neu.pdf
    Download Restriction: no
    ---><---

    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, September.
    3. Imai, Haruo, 1983. "Individual Monotonicity and Lexicographic Maxmin Solution," Econometrica, Econometric Society, vol. 51(2), pages 389-401, March.
    4. Nash, John, 1950. "The Bargaining Problem," Econometrica, Econometric Society, vol. 18(2), pages 155-162, April.
    5. Dubra, Juan, 2001. "An asymmetric Kalai-Smorodinsky solution," Economics Letters, Elsevier, vol. 73(2), pages 131-136, November.
    6. Roth, Alvin E., 1977. "Independence of irrelevant alternatives, and solutions to Nash's bargaining problem," Journal of Economic Theory, Elsevier, vol. 16(2), pages 247-251, December.
    7. Driesen, Bram, 2012. "Proportional concessions and the leximin solution," Economics Letters, Elsevier, vol. 114(3), pages 288-291.
    8. 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.
    9. 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.
    10. Chun, Youngsub & Peters, Hans, 1991. "The lexicographic equal-loss solution," Mathematical Social Sciences, Elsevier, vol. 22(2), pages 151-161, October.
    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, 2013. "Stagnation proofness and individually monotonic bargaining solutions," Working Papers 2013/04, Economics Department, Universitat Jaume I, Castellón (Spain).

    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, 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. Driesen, Bram, 2012. "Proportional concessions and the leximin solution," Economics Letters, Elsevier, vol. 114(3), pages 288-291.
    4. Carlos Alós-Ferrer & Jaume García-Segarra & Miguel Ginés-Vilar, 2018. "Anchoring on Utopia: a generalization of the Kalai–Smorodinsky solution," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 6(2), pages 141-155, October.
    5. Dubra, Juan, 2001. "An asymmetric Kalai-Smorodinsky solution," Economics Letters, Elsevier, vol. 73(2), pages 131-136, November.
    6. 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.
    7. 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.
    8. 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.
    9. 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.
    10. Dittrich, Marcus & Städter, Silvio, 2015. "Moral hazard and bargaining over incentive contracts," Research in Economics, Elsevier, vol. 69(1), pages 75-85.
    11. Driesen, Bram, 2016. "Truncated Leximin solutions," Mathematical Social Sciences, Elsevier, vol. 83(C), pages 79-87.
    12. Jaume García-Segarra & Miguel Ginés-Vilar, 2013. "Stagnation proofness and individually monotonic bargaining solutions," Working Papers 2013/04, Economics Department, Universitat Jaume I, Castellón (Spain).
    13. del Carmen Marco Gil, M., 1995. "Efficient solutions for bargaining problems with claims," Mathematical Social Sciences, Elsevier, vol. 30(1), pages 57-69, August.
    14. 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.
    15. 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.
    16. Laruelle, Annick & Valenciano, Federico, 2007. "Bargaining in committees as an extension of Nash's bargaining theory," Journal of Economic Theory, Elsevier, vol. 132(1), pages 291-305, January.
    17. 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..
    18. Mariotti, Marco, 1996. "Non-optimal Nash Bargaining Solutions," Economics Letters, Elsevier, vol. 52(1), pages 15-20, July.
    19. Shiran Rachmilevitch, 2017. "Axiomatizations of the equal-loss and weighted equal-loss bargaining solutions," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 49(1), pages 1-9, June.
    20. 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.

    More about this item

    Keywords

    Bargaining; asymmetric bargaining solution; leximin solution;
    All these keywords.

    JEL classification:

    • 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:awi:wpaper:0523. 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: Gabi Rauscher (email available below). General contact details of provider: https://edirc.repec.org/data/awheide.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.