IDEAS home Printed from https://ideas.repec.org/p/bie/wpaper/366.html
   My bibliography  Save this paper

Two support results for the Kalai-Smorodinsky solution in small object division markets

Author

Listed:
  • Haake, Claus-Jochen

    (Center for Mathematical Economics, Bielefeld University)

Abstract

We discuss two support results for the Kalai-Smorodinsky bargaining solution in the context of an object division problem involving two agents. Allocations of objects resulting from strategic interaction are obtained as a demand vector in a specific market. For the first support result games in strategic form are derived that exhibit a unique Nash equilibrium. The second result uses subgame perfect equlibria of a game in extensive form. Although there may be multiple equilibria, coordination problems can be removed.

Suggested Citation

  • Haake, Claus-Jochen, 2011. "Two support results for the Kalai-Smorodinsky solution in small object division markets," Center for Mathematical Economics Working Papers 366, Center for Mathematical Economics, Bielefeld University.
    • Handle: RePEc:bie:wpaper:366
    as

    Download full text from publisher

    File URL: https://pub.uni-bielefeld.de/download/2315428/2319788
    File Function: First Version, 2005
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Serrano, Roberto, 1997. "A comment on the Nash program and the theory of implementation," Economics Letters, Elsevier, vol. 55(2), pages 203-208, August.
    2. Roberto Serrano, 2005. "Fifty years of the Nash program, 1953-2003," Investigaciones Economicas, Fundación SEPI, vol. 29(2), pages 219-258, May.
    3. Nash, John, 1953. "Two-Person Cooperative Games," Econometrica, Econometric Society, vol. 21(1), pages 128-140, April.
    4. Dagan, Nir & Serrano, Roberto, 1998. "Invariance and randomness in the Nash program for coalitional games," Economics Letters, Elsevier, vol. 58(1), pages 43-49, January.
    5. Moulin, H., 1984. "Implementing the Kalai-Smorodinsky bargaining solution," Journal of Economic Theory, Elsevier, vol. 33(1), pages 32-45, June.
    6. Kalai, Ehud & Smorodinsky, Meir, 1975. "Other Solutions to Nash's Bargaining Problem," Econometrica, Econometric Society, vol. 43(3), pages 513-518, May.
    7. Claus-Jochen Haake & Walter Trockel, 2010. "On Maskin monotonicity of solution based social choice rules," Review of Economic Design, Springer;Society for Economic Design, vol. 14(1), pages 17-25, March.
    8. Bergin, James & Duggan, John, 1999. "An Implementation-Theoretic Approach to Non-cooperative Foundations," Journal of Economic Theory, Elsevier, vol. 86(1), pages 50-76, May.
    9. Walter Trockel, 2002. "Integrating the Nash program into mechanism theory," Review of Economic Design, Springer;Society for Economic Design, vol. 7(1), pages 27-43.
    10. Demange, Gabrielle, 1984. "Implementing Efficient Egalitarian Equivalent Allocations," Econometrica, Econometric Society, vol. 52(5), pages 1167-1177, September.
    11. Rosenmüller, Joachim & Trockel, Walter, 2017. "Game theory," Center for Mathematical Economics Working Papers 321, Center for Mathematical Economics, Bielefeld University.
    12. Miyagawa, Eiichi, 2002. "Subgame-perfect implementation of bargaining solutions," Games and Economic Behavior, Elsevier, vol. 41(2), pages 292-308, November.
    13. Trockel, Walter, 2017. "Unique Nash implementation for a class of bargaining solutions," Center for Mathematical Economics Working Papers 308, Center for Mathematical Economics, Bielefeld University.
    14. Haake, Claus-Jochen, 2017. "Implementation of the Kalai Smorodinski bargaining solution in dominant strategies," Center for Mathematical Economics Working Papers 301, Center for Mathematical Economics, Bielefeld University.
    15. Walter Trockel, 2000. "Implementations of the Nash solution based on its Walrasian characterization," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 16(2), pages 277-294.
    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. Claus-Jochen Haake & Walter Trockel, 2020. "Introduction to the Special Issue “Bargaining”," Homo Oeconomicus: Journal of Behavioral and Institutional Economics, Springer, vol. 37(1), pages 1-6, November.
    2. Roberto Serrano, 2021. "Sixty-seven years of the Nash program: time for retirement?," SERIEs: Journal of the Spanish Economic Association, Springer;Spanish Economic Association, vol. 12(1), pages 35-48, March.
    3. Claus-Jochen Haake & Walter Trockel, 2021. "Socio-legal Systems and Implementation of the Nash Solution in Debreu-Hurwicz Equilibrium," Working Papers CIE 140, Paderborn University, CIE Center for International Economics.
    4. Claus-Jochen Haake & Walter Trockel, 2022. "Socio-legal systems and implementation of the Nash solution in Debreu–Hurwicz equilibrium," Review of Economic Design, Springer;Society for Economic Design, vol. 26(4), pages 635-649, December.
    5. Haake, Claus-Jochen & Trockel, Walter, 2021. "Socio-legal Systems and Implementation of the Nash Solution in Debreu-Hurwicz Equilibrium," Center for Mathematical Economics Working Papers 647, Center for Mathematical Economics, Bielefeld University.

    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. Roberto Serrano, 2005. "Fifty years of the Nash program, 1953-2003," Investigaciones Economicas, Fundación SEPI, vol. 29(2), pages 219-258, May.
    2. Claus-Jochen Haake & Walter Trockel, 2010. "On Maskin monotonicity of solution based social choice rules," Review of Economic Design, Springer;Society for Economic Design, vol. 14(1), pages 17-25, March.
    3. Trockel, Walter, 2017. "Can and should the Nash Program be looked at as a part of mechanism theory," Center for Mathematical Economics Working Papers 322, Center for Mathematical Economics, Bielefeld University.
    4. Walter Trockel, 2002. "Integrating the Nash program into mechanism theory," Review of Economic Design, Springer;Society for Economic Design, vol. 7(1), pages 27-43.
    5. Papatya Duman & Walter Trockel, 2016. "On non-cooperative foundation and implementation of the Nash solution in subgame perfect equilibrium via Rubinstein's game," The Journal of Mechanism and Institution Design, Society for the Promotion of Mechanism and Institution Design, University of York, vol. 1(1), pages 83-107, December.
    6. Trockel, Walter, 2011. "An exact non-cooperative support for the sequential Raiffa solution," Journal of Mathematical Economics, Elsevier, vol. 47(1), pages 77-83, January.
    7. Walter Trockel, 1999. "On the Nash Program for the Nash Bargaining Solution," UCLA Economics Working Papers 788, UCLA Department of Economics.
    8. Claus-Jochen Haake & Walter Trockel, 2022. "Socio-legal systems and implementation of the Nash solution in Debreu–Hurwicz equilibrium," Review of Economic Design, Springer;Society for Economic Design, vol. 26(4), pages 635-649, December.
    9. Kang Rong, 2018. "Fair Allocation When Players' Preferences Are Unknown," Economic Inquiry, Western Economic Association International, vol. 56(1), pages 497-509, January.
    10. Roberto Serrano, 2021. "Sixty-seven years of the Nash program: time for retirement?," SERIEs: Journal of the Spanish Economic Association, Springer;Spanish Economic Association, vol. 12(1), pages 35-48, March.
    11. Claus-Jochen Haake & Walter Trockel, 2020. "Introduction to the Special Issue “Bargaining”," Homo Oeconomicus: Journal of Behavioral and Institutional Economics, Springer, vol. 37(1), pages 1-6, November.
    12. Trockel, Walter, 2017. "Unique Nash implementation for a class of bargaining solutions," Center for Mathematical Economics Working Papers 308, Center for Mathematical Economics, Bielefeld University.
    13. Michele Lombardi & Naoki Yoshihara, 2020. "Partially-honest Nash implementation: a full characterization," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 70(3), pages 871-904, October.
    14. Johannes Spinnewijn & Frans Spinnewyn, 2015. "Revising claims and resisting ultimatums in bargaining problems," Review of Economic Design, Springer;Society for Economic Design, vol. 19(2), pages 91-116, June.
    15. Gomez, Juan Camilo, 2006. "Achieving efficiency with manipulative bargainers," Games and Economic Behavior, Elsevier, vol. 57(2), pages 254-263, November.
    16. Hannu Vartiainen, 2007. "Nash implementation and the bargaining problem," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 29(2), pages 333-351, September.
    17. 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.
    18. Yakov Babichenko & Leonard J. Schulman, 2015. "Pareto Efficient Nash Implementation Via Approval Voting," Papers 1502.05238, arXiv.org, revised Mar 2017.
    19. Chessa, Michela & Hanaki, Nobuyuki & Lardon, Aymeric & Yamada, Takashi, 2023. "An experiment on the Nash program: A comparison of two strategic mechanisms implementing the Shapley value," Games and Economic Behavior, Elsevier, vol. 141(C), pages 88-104.
    20. Ju, Yuan, 2012. "Reject and renegotiate: The Shapley value in multilateral bargaining," Journal of Mathematical Economics, Elsevier, vol. 48(6), pages 431-436.

    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:bie:wpaper:366. 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: Bettina Weingarten (email available below). General contact details of provider: https://edirc.repec.org/data/imbiede.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.