IDEAS home Printed from https://ideas.repec.org/a/spr/annopr/v332y2024i1d10.1007_s10479-023-05713-8.html
   My bibliography  Save this article

The $$\kappa $$ κ -core and the $$\kappa $$ κ -balancedness of TU games

Author

Listed:
  • David Bartl

    (Silesian University in Opava)

  • Miklós Pintér

    (Corvinus University of Budapest)

Abstract

We consider transferable utility cooperative games with infinitely many players. In particular, we generalize the notions of core and balancedness, and also the Bondareva–Shapley Theorem for infinite TU games with and without restricted cooperation, to the cases where the core consists of $$\kappa $$ κ -additive set functions. Our generalized Bondareva–Shapley Theorem extends previous results by Bondareva (Problemy Kibernetiki 10:119–139, 1963), Shapley (Naval Res Logist Q 14:453–460, 1967), Schmeidler (On balanced games with infinitely many players, The Hebrew University, Jerusalem, 1967), Faigle (Zeitschrift für Oper Res 33(6):405–422, 1989), Kannai (J Math Anal Appl 27:227–240, 1969; The core and balancedness, handbook of game theory with economic applications, North-Holland, 1992), Pintér (Linear Algebra Appl 434(3):688–693, 2011) and Bartl and Pintér (Oper Res Lett 51(2):153–158, 2023).

Suggested Citation

  • David Bartl & Miklós Pintér, 2024. "The $$\kappa $$ κ -core and the $$\kappa $$ κ -balancedness of TU games," Annals of Operations Research, Springer, vol. 332(1), pages 689-703, January.
    • Handle: RePEc:spr:annopr:v:332:y:2024:i:1:d:10.1007_s10479-023-05713-8
    DOI: 10.1007/s10479-023-05713-8
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10479-023-05713-8
    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/s10479-023-05713-8?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

    for a different version of it.

    References listed on IDEAS

    as
    1. Michel Grabisch & Pedro Miranda, 2008. "On the vertices of the k-additive core," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) hal-00321625, HAL.
    2. Bezalel Peleg & Peter Sudhölter, 2007. "Introduction to the Theory of Cooperative Games," Theory and Decision Library C, Springer, edition 0, number 978-3-540-72945-7, July.
    3. Kannai, Yakar, 1992. "The core and balancedness," 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 12, pages 355-395, Elsevier.
    4. Lloyd S. Shapley, 1967. "On balanced sets and cores," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 14(4), pages 453-460.
    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. Zhe Yang, 2025. "The cooperative analysis of oligopoly TU markets with infinitely many firms," Annals of Operations Research, Springer, vol. 345(1), pages 517-532, February.

    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. Stéphane Gonzalez & Michel Grabisch, 2015. "Autonomous coalitions," Annals of Operations Research, Springer, vol. 235(1), pages 301-317, December.
    2. Gonzalez, Stéphane & Grabisch, Michel, 2016. "Multicoalitional solutions," Journal of Mathematical Economics, Elsevier, vol. 64(C), pages 1-10.
    3. Michel Grabisch & Peter Sudhölter, 2012. "The bounded core for games with precedence constraints," Annals of Operations Research, Springer, vol. 201(1), pages 251-264, December.
    4. Predtetchinski, Arkadi & Jean-Jacques Herings, P., 2004. "A necessary and sufficient condition for non-emptiness of the core of a non-transferable utility game," Journal of Economic Theory, Elsevier, vol. 116(1), pages 84-92, May.
    5. Pisciella, Paolo & Gaivoronski, Alexei A., 2024. "Modeling collaborative data service provision around an open source platform under uncertainty with stochastic provision games," Omega, Elsevier, vol. 129(C).
    6. Jean Guillaume Forand & Metin Uyanık, 2019. "Fixed-point approaches to the proof of the Bondareva–Shapley Theorem," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 7(1), pages 117-124, May.
    7. Kaneko, Takuto & Nakada, Satoshi, 2025. "Nullified-game consistency and axiomatizations of the Core of TU-games with a fixed player set," Economics Letters, Elsevier, vol. 250(C).
    8. Xiaowei Lin & Jing Zhou & Lianmin Zhang & Yinlian Zeng, 2021. "Revenue sharing for resource reallocation among project activity contractors," Annals of Operations Research, Springer, vol. 301(1), pages 121-141, June.
    9. Stéphane Gonzalez & Michel Grabisch, 2015. "Preserving coalitional rationality for non-balanced games," International Journal of Game Theory, Springer;Game Theory Society, vol. 44(3), pages 733-760, August.
    10. Moshe Babaioff & Uriel Feige, 2019. "A New Approach to Fair Distribution of Welfare," Papers 1909.11346, arXiv.org.
    11. Bloch, Francis & de Clippel, Geoffroy, 2010. "Cores of combined games," Journal of Economic Theory, Elsevier, vol. 145(6), pages 2424-2434, November.
    12. repec:hal:pseose:halshs-00881108 is not listed on IDEAS
    13. Pedro Calleja & Carles Rafels & Stef Tijs, 2010. "Aggregate monotonic stable single-valued solutions for cooperative games," Working Papers in Economics 237, Universitat de Barcelona. Espai de Recerca en Economia.
    14. Elena Parilina & Leon Petrosyan, 2020. "On a Simplified Method of Defining Characteristic Function in Stochastic Games," Mathematics, MDPI, vol. 8(7), pages 1-14, July.
    15. Ketelaars, Martijn & Borm, Peter & Kort, Peter M., 2023. "Dynamic Stability of Cooperative Investment under Uncertainty," Discussion Paper 2023-023, Tilburg University, Center for Economic Research.
    16. repec:hal:pseose:halshs-01235632 is not listed on IDEAS
    17. Takaaki Abe & Satoshi Nakada, 2023. "Core stability of the Shapley value for cooperative games," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 60(4), pages 523-543, May.
    18. Shuige Liu, 2018. "Information Sufficiency and the Core," Papers 1802.04595, arXiv.org, revised Aug 2025.
    19. Milan Studený & Václav Kratochvíl, 2022. "Facets of the cone of exact games," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 95(1), pages 35-80, February.
    20. Xinyang Wang, 2020. "Cooperation in Small Groups -- an Optimal Transport Approach," Papers 2005.11244, arXiv.org.
    21. Fatma Aslan & Papatya Duman & Walter Trockel, 2020. "Non-cohesive TU-games: Duality and P-core," Working Papers CIE 136, Paderborn University, CIE Center for International Economics.
    22. 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.

    More about this item

    Keywords

    ;
    ;
    ;
    ;
    ;
    ;

    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:annopr:v:332:y:2024:i:1:d:10.1007_s10479-023-05713-8. 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.