IDEAS home Printed from https://ideas.repec.org/a/spr/jogath/v30y2001i1p117-139.html
   My bibliography  Save this article

The semireactive bargaining set of a cooperative game

Author

Listed:
  • Peter Sudhölter
  • Jos A. M. Potters

Abstract

The semireactive bargaining set, a solution for cooperative games, is introduced. This solution is in general a subsolution of the bargaining set and a supersolution of the reactive bargaining set. However, on various classes of transferable utility games the semireactive and the reactive bargaining set coincide. The semireactive prebargaining set on TU games can be axiomatized by one-person rationality, the reduced game property, a weak version of the converse reduced game property with respect to subgrand coalitions, and subgrand stability. Furthermore, it is shown that there is a suitable weakening of subgrand stability, which allows to characterize the prebargaining set. Replacing the reduced game by the imputation saving reduced game and employing individual rationality as an additional axiom yields characterizations of both, the bargaining set and the semireactive bargaining set.

Suggested Citation

  • Peter Sudhölter & Jos A. M. Potters, 2001. "The semireactive bargaining set of a cooperative game," International Journal of Game Theory, Springer;Game Theory Society, vol. 30(1), pages 117-139.
    • Handle: RePEc:spr:jogath:v:30:y:2001:i:1:p:117-139
    Note: Received September 2000/Revised version June 2001
    as

    Download full text from publisher

    File URL: http://link.springer.de/link/service/journals/00182/papers/1030001/10300117.pdf
    Download Restriction: Access to the full text of the articles in this series is restricted
    ---><---

    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. Peleg, B, 1986. "On the Reduced Game Property and Its Converse," International Journal of Game Theory, Springer;Game Theory Society, vol. 15(3), pages 187-200.
    2. Peter Sudhölter & Bezalel Peleg, 2000. "The Positive Prekernel Of A Cooperative Game," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 2(04), pages 287-305.
    3. TamÂs Solymosi, 1999. "On the bargaining set, kernel and core of superadditive games," International Journal of Game Theory, Springer;Game Theory Society, vol. 28(2), pages 229-240.
    4. Peleg, Bezalel, 1992. "Axiomatizations of the core," Handbook of Game Theory with Economic Applications, in: R.J. Aumann & S. Hart (ed.), Handbook of Game Theory with Economic Applications, edition 1, volume 1, chapter 13, pages 397-412, Elsevier.
    5. Chris Snijders, 1995. "Axiomatization of the Nucleolus," Mathematics of Operations Research, INFORMS, vol. 20(1), pages 189-196, February.
    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. Morelli, Massimo & Montero, Maria, 2003. "The demand bargaining set: general characterization and application to majority games," Games and Economic Behavior, Elsevier, vol. 42(1), pages 137-155, January.
    2. Tamás Solymosi, 2008. "Bargaining sets and the core in partitioning games," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 16(4), pages 425-440, December.
    3. Guni Orshan & Peter Sudhölter, 2010. "The positive core of a cooperative game," International Journal of Game Theory, Springer;Game Theory Society, vol. 39(1), pages 113-136, March.
    4. Michel Grabisch & Hervé Moulin & José Manuel Zarzuelo, 2024. "Professor Peter Sudhölter (1957–2024)," International Journal of Game Theory, Springer;Game Theory Society, vol. 53(2), pages 289-294, June.
    5. Daniel Granot, 2010. "The reactive bargaining set for cooperative games," International Journal of Game Theory, Springer;Game Theory Society, vol. 39(1), pages 163-170, March.
    6. Josep M. Izquierdo & Carles Rafels, 2010. "On the coincidence between the Shimomuras bargaining sets and the core," Working Papers in Economics 241, Universitat de Barcelona. Espai de Recerca en Economia.
    7. Josep M Izquierdo & Carles Rafels, 2012. "On the coincidence of the core and the bargaining sets," Economics Bulletin, AccessEcon, vol. 32(3), pages 2035-2043.

    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. Guni Orshan & Peter Sudhölter, 2012. "Nonsymmetric variants of the prekernel and the prenucleolus," International Journal of Game Theory, Springer;Game Theory Society, vol. 41(4), pages 809-828, November.
    2. Ichiro Nishizaki & Tomohiro Hayashida & Yuki Shintomi, 2016. "A core-allocation for a network restricted linear production game," Annals of Operations Research, Springer, vol. 238(1), pages 389-410, March.
    3. Francesc Llerena & Carles Rafels, 2007. "Convex decomposition of games and axiomatizations of the core and the D-core," International Journal of Game Theory, Springer;Game Theory Society, vol. 35(4), pages 603-615, April.
    4. John Kleppe & Hans Reijnierse & Peter Sudhölter, 2016. "Axiomatizations of symmetrically weighted solutions," Annals of Operations Research, Springer, vol. 243(1), pages 37-53, August.
    5. Ichiro Nishizaki & Tomohiro Hayashida & Yuki Shintomi, 2016. "A core-allocation for a network restricted linear production game," Annals of Operations Research, Springer, vol. 238(1), pages 389-410, March.
    6. Guni Orshan & Peter Sudhölter, 2010. "The positive core of a cooperative game," International Journal of Game Theory, Springer;Game Theory Society, vol. 39(1), pages 113-136, March.
    7. Roberto Serrano & Ken Ichi Shimomura, 1996. "An axiomatization of the prekernel of nontransferable utility games," Economics Working Papers 167, Department of Economics and Business, Universitat Pompeu Fabra.
    8. Hokari, Toru & Kibris, Ozgur, 2003. "Consistency, converse consistency, and aspirations in TU-games," Mathematical Social Sciences, Elsevier, vol. 45(3), pages 313-331, July.
    9. Nizamogullari, Duygu & Özkal-Sanver, İpek, 2014. "Characterization of the core in full domain marriage problems," Mathematical Social Sciences, Elsevier, vol. 69(C), pages 34-42.
    10. Gooni Orshan & Peter Sudholter, 2001. "Reconfirming the Prenucleolus," Discussion Paper Series dp267, The Federmann Center for the Study of Rationality, the Hebrew University, Jerusalem.
    11. Rogna, Marco, 2021. "The central core and the mid-central core as novel set-valued and point-valued solution concepts for transferable utility coalitional games," Mathematical Social Sciences, Elsevier, vol. 109(C), pages 1-11.
    12. Stefan Engevall & Maud Göthe-Lundgren & Peter Värbrand, 2004. "The Heterogeneous Vehicle-Routing Game," Transportation Science, INFORMS, vol. 38(1), pages 71-85, February.
    13. E. Calvo & E. Gutiérrez, 1996. "A prekernel characterization by means of stability properties," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 4(2), pages 257-267, December.
    14. Nunez, Marina & Rafels, Carles, 2003. "Characterization of the extreme core allocations of the assignment game," Games and Economic Behavior, Elsevier, vol. 44(2), pages 311-331, August.
    15. Camelia Bejan & Juan Gómez, 2012. "Axiomatizing core extensions," International Journal of Game Theory, Springer;Game Theory Society, vol. 41(4), pages 885-898, November.
    16. Nir Dagan, 1995. "Consistent Solutions in Exchange Economies: a Characterization of the Price Mechanism," Economic theory and game theory 011, Nir Dagan.
    17. Sylvain Béal & Stéphane Gonzalez & Philippe Solal & Peter Sudhölter, 2023. "Axiomatic characterizations of the core without consistency," International Journal of Game Theory, Springer;Game Theory Society, vol. 52(3), pages 687-701, September.
    18. repec:ebl:ecbull:v:3:y:2008:i:70:p:1-8 is not listed on IDEAS
    19. Peleg, Bezalel & Tijs, Stef, 1996. "The Consistency Principle for Games in Strategic Forms," International Journal of Game Theory, Springer;Game Theory Society, vol. 25(1), pages 13-34.
    20. William Thomson, 2011. "Consistency and its converse: an introduction," Review of Economic Design, Springer;Society for Economic Design, vol. 15(4), pages 257-291, December.
    21. Ata Atay & Eric Bahel & Tamás Solymosi, 2023. "Matching markets with middlemen under transferable utility," Annals of Operations Research, Springer, vol. 322(2), pages 539-563, March.

    More about this item

    Keywords

    TU game; bargaining set;

    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:spr:jogath:v:30:y:2001:i:1:p:117-139. 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.