IDEAS home Printed from https://ideas.repec.org/a/spr/joptap/v145y2010i3d10.1007_s10957-010-9697-y.html
   My bibliography  Save this article

Kalai-Smorodinsky Bargaining Solution Equilibria

Author

Listed:
  • G. De Marco

    (Università di Napoli Parthenope)

  • J. Morgan

    (Università di Napoli Federico II)

Abstract

Multicriteria games describe strategic interactions in which players, having more than one criterion to take into account, don’t have an a-priori opinion on the relative importance of all these criteria. Roemer (Econ. Bull. 3:1–13, 2005) introduces an organizational interpretation of the concept of equilibrium: each player can be viewed as running a bargaining game among criteria. In this paper, we analyze the bargaining problem within each player by considering the Kalai-Smorodinsky bargaining solution (see Kalai and Smorodinsky in Econometrica 43:513–518, 1975). We provide existence results for the so called Kalai-Smorodinsky bargaining solution equilibria for a general class of disagreement points which properly includes the one considered by Roemer (Econ. Bull. 3:1–13, 2005). Moreover we look at the refinement power of this equilibrium concept and show that it is an effective selection device even when combined with classical refinement concepts based on stability with respect to perturbations; in particular, we consider the extension to multicriteria games of the Selten’s trembling hand perfect equilibrium concept (see Selten in Int. J. Game Theory 4:25–55, 1975) and prove that perfect Kalai-Smorodinsky bargaining solution equilibria exist and properly refine both the perfect equilibria and the Kalai-Smorodinsky bargaining solution equilibria.

Suggested Citation

  • G. De Marco & J. Morgan, 2010. "Kalai-Smorodinsky Bargaining Solution Equilibria," Journal of Optimization Theory and Applications, Springer, vol. 145(3), pages 429-449, June.
    • Handle: RePEc:spr:joptap:v:145:y:2010:i:3:d:10.1007_s10957-010-9697-y
    DOI: 10.1007/s10957-010-9697-y
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10957-010-9697-y
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s10957-010-9697-y?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 look for a different version below or search for a different version of it.

    Other versions of this item:

    References listed on IDEAS

    as
    1. 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.
    2. Peter Borm & Freek van Megen & Stef Tijs, 1999. "A perfectness concept for multicriteria games," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 49(3), pages 401-412, July.
    3. Jacqueline Morgan, 2005. "Approximations and Well-Posedness in Multicriteria Games," Annals of Operations Research, Springer, vol. 137(1), pages 257-268, July.
    4. Giuseppe De Marco & Jacqueline Morgan, 2007. "A Refinement Concept For Equilibria In Multicriteria Games Via Stable Scalarizations," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 9(02), pages 169-181.
    5. Kalai, Ehud & Smorodinsky, Meir, 1975. "Other Solutions to Nash's Bargaining Problem," Econometrica, Econometric Society, vol. 43(3), pages 513-518, May.
    6. Nash, John, 1950. "The Bargaining Problem," Econometrica, Econometric Society, vol. 18(2), pages 155-162, April.
    7. Loridan, P. & Morgan, J. & Raucci, R., 1997. "Convergence of Minimal and Approximate Minimal Elements of Sets in Partially Ordered Vector Spaces," Papiers d'Economie Mathématique et Applications 97.94, Université Panthéon-Sorbonne (Paris 1).
    8. John Roemer, 2005. "Games with vector-valued payoffs and their application to competition between organizations," Economics Bulletin, AccessEcon, vol. 3(16), pages 1-13.
    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. Bas Dietzenbacher & Hans Peters, 2022. "Characterizing NTU-bankruptcy rules using bargaining axioms," Annals of Operations Research, Springer, vol. 318(2), pages 871-888, November.
    2. Driesen, Bram, 2012. "Proportional concessions and the leximin solution," Economics Letters, Elsevier, vol. 114(3), pages 288-291.
    3. Rudolf Vetschera & Michael Filzmoser & Ronald Mitterhofer, 2014. "An Analytical Approach to Offer Generation in Concession-Based Negotiation Processes," Group Decision and Negotiation, Springer, vol. 23(1), pages 71-99, January.
    4. Giuseppe De Marco & Jacqueline Morgan, 2009. "On Multicriteria Games with Uncountable Sets of Equilibria," CSEF Working Papers 242, Centre for Studies in Economics and Finance (CSEF), University of Naples, Italy.
    5. Özgür Kıbrıs, 2012. "Nash bargaining in ordinal environments," Review of Economic Design, Springer;Society for Economic Design, vol. 16(4), pages 269-282, December.
    6. Emililo Calvo, 2004. "Single NTU-value solutions," Game Theory and Information 0405004, University Library of Munich, Germany, revised 10 Jun 2004.
    7. 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.
    8. Vincent Martinet & Pedro Gajardo & Michel de Lara, 2021. "Bargaining On Monotonic Economic Environments," Working Papers hal-03206724, HAL.
    9. Barry Nalebuff, 2021. "A Perspective-Invariant Approach to Nash Bargaining," Management Science, INFORMS, vol. 67(1), pages 577-593, January.
    10. 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.
    11. 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.
    12. del Carmen Marco Gil, M., 1995. "Efficient solutions for bargaining problems with claims," Mathematical Social Sciences, Elsevier, vol. 30(1), pages 57-69, August.
    13. Dubra, Juan, 2001. "An asymmetric Kalai-Smorodinsky solution," Economics Letters, Elsevier, vol. 73(2), pages 131-136, November.
    14. Naeve-Steinweg, E., 2004. "The averaging mechanism," Games and Economic Behavior, Elsevier, vol. 46(2), pages 410-424, February.
    15. 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.
    16. 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.
    17. Lea Melnikovová, 2017. "Can Game Theory Help to Mitigate Water Conflicts in the Syrdarya Basin?," Acta Universitatis Agriculturae et Silviculturae Mendelianae Brunensis, Mendel University Press, vol. 65(4), pages 1393-1401.
    18. Daniele Cassese & Paolo Pin, 2018. "Decentralized Pure Exchange Processes on Networks," Papers 1803.08836, arXiv.org, revised Mar 2022.
    19. 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.
    20. Takeuchi, Ai & Veszteg, Róbert F. & Kamijo, Yoshio & Funaki, Yukihiko, 2022. "Bargaining over a jointly produced pie: The effect of the production function on bargaining outcomes," Games and Economic Behavior, Elsevier, vol. 134(C), pages 169-198.

    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:spr:joptap:v:145:y:2010:i:3:d:10.1007_s10957-010-9697-y. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.