IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v11y2023i13p2812-d1177158.html
   My bibliography  Save this article

Non-Emptiness, Relative Coincidences and Axiomatic Results for the Precore

Author

Listed:
  • Yan-An Hwang

    (Department of Applied Mathematics, National Dong Hwa University, Hualien 974, Taiwan)

  • Yu-Hsien Liao

    (Department of Applied Mathematics, National Pingtung University, Pingtung 900, Taiwan)

Abstract

Taking into account the definition of the precore, we initially analyze its non-emptiness using duality results from linear programming theory. We then introduce the dominance core to investigate the coincident relations between the precore and dominance core. Finally, we propose specific reduction approaches to axiomatize the precore.

Suggested Citation

  • Yan-An Hwang & Yu-Hsien Liao, 2023. "Non-Emptiness, Relative Coincidences and Axiomatic Results for the Precore," Mathematics, MDPI, vol. 11(13), pages 1-12, June.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:13:p:2812-:d:1177158
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/11/13/2812/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/11/13/2812/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Achille Basile & Vincenzo Scalzo, 2020. "Non-emptiness of the alpha-core: sufficient and necessary conditions," International Journal of Game Theory, Springer;Game Theory Society, vol. 49(4), pages 1143-1153, December.
    2. repec:ebl:ecbull:v:3:y:2005:i:14:p:1-8 is not listed on IDEAS
    3. Serrano, Roberto & Volij, Oscar, 1998. "Axiomatizations of neoclassical concepts for economies," Journal of Mathematical Economics, Elsevier, vol. 30(1), pages 87-108, August.
    4. Chih Chang, 2000. "Note: Remarks on theory of the core," Naval Research Logistics (NRL), John Wiley & Sons, vol. 47(5), pages 455-458, August.
    5. Tadenuma, K, 1992. "Reduced Games, Consistency, and the Core," International Journal of Game Theory, Springer;Game Theory Society, vol. 20(4), pages 325-334.
    6. Lloyd S. Shapley, 1967. "On balanced sets and cores," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 14(4), pages 453-460.
    7. 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.
    8. Yu-Hsien Liao, 2018. "The precore: converse consistent enlargements and alternative axiomatic results," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 26(1), pages 146-163, April.
    9. Juan Carlos Cesco, 2009. "A Necessary And Sufficient Condition For The Non-Emptiness Of The Socially Stable Core In Structuredtu-Games," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 11(03), pages 383-389.
    10. Morton Davis & Michael Maschler, 1965. "The kernel of a cooperative game," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 12(3), pages 223-259, September.
    11. Yan-An Hwang, 2005. "The coincidence of the core and the dominance core on multi-choice games," Economics Bulletin, AccessEcon, vol. 3(14), pages 1-8.
    12. Voorneveld, Mark & van den Nouweland, Anne, 1998. "A new axiomatization of the core of games with transferable utility," Economics Letters, Elsevier, vol. 60(2), pages 151-155, August.
    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. Toru Hokari & Yukihiko Funaki & Peter Sudhölter, 2020. "Consistency, anonymity, and the core on the domain of convex games," Review of Economic Design, Springer;Society for Economic Design, vol. 24(3), pages 187-197, December.
    2. Camelia Bejan & Juan Camilo Gómez & Anne van den Nouweland, 2022. "On the importance of reduced games in axiomatizing core extensions," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 59(3), pages 637-668, October.
    3. Camelia Bejan & Juan Gómez, 2012. "Axiomatizing core extensions," International Journal of Game Theory, Springer;Game Theory Society, vol. 41(4), pages 885-898, November.
    4. 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.
    5. Yang, Jian & Li, Jianbin, 2020. "Cooperative game with nondeterministic returns," Journal of Mathematical Economics, Elsevier, vol. 88(C), pages 123-140.
    6. Yu-Hsien Liao, 2008. "Consistency and the core for fuzzy non-transferable-utility games," Economics Bulletin, AccessEcon, vol. 3(45), pages 1-6.
    7. Ling-Yun Chung & Yu-Hsien Liao, 2014. "A Consistent Allocation Rule: Non-emptiness, Reductions, Domination and Axiomatization," Review of Economics & Finance, Better Advances Press, Canada, vol. 4, pages 61-74, November.
    8. 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.
    9. M. Albizuri & Peter Sudhölter, 2016. "Characterizations of the core of TU and NTU games with communication structures," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 46(2), pages 451-475, February.
    10. repec:ebl:ecbull:v:3:y:2008:i:45:p:1-6 is not listed on IDEAS
    11. Yu-Hsien Liao, 2018. "The precore: converse consistent enlargements and alternative axiomatic results," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 26(1), pages 146-163, April.
    12. Yu-Hsien Liao, 2012. "Converse consistent enlargements of the unit-level-core of the multi-choice 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. 20(4), pages 743-753, December.
    13. Pedro Calleja & Francesc Llerena & Peter Sudhölter, 2020. "Monotonicity and Weighted Prenucleoli: A Characterization Without Consistency," Mathematics of Operations Research, INFORMS, vol. 45(3), pages 1056-1068, August.
    14. Dietzenbacher, Bas & Borm, Peter & Hendrickx, Ruud, 2017. "The procedural egalitarian solution," Games and Economic Behavior, Elsevier, vol. 106(C), pages 179-187.
    15. Dietzenbacher, Bas & Yanovskaya, Elena, 2023. "The equal split-off set for NTU-games," Mathematical Social Sciences, Elsevier, vol. 121(C), pages 61-67.
    16. Luisa Carpente & Balbina Casas-Méndez & Ignacio García-Jurado & Anne Nouweland, 2010. "The truncated core for games with upper bounds," International Journal of Game Theory, Springer;Game Theory Society, vol. 39(4), pages 645-656, October.
    17. Bas Dietzenbacher & Elena Yanovskaya, 2021. "Consistency of the equal split-off set," International Journal of Game Theory, Springer;Game Theory Society, vol. 50(1), pages 1-22, March.
    18. Ning Sun & Zaifu Yang, 2016. "A Theory of Marriage with Mutually Consented Divorces," Discussion Papers 16/14, Department of Economics, University of York.
    19. Csóka, Péter & Herings, P. Jean-Jacques, 2014. "Risk allocation under liquidity constraints," Journal of Banking & Finance, Elsevier, vol. 49(C), pages 1-9.
    20. Bejan, Camelia & Gómez, Juan Camilo & van den Nouweland, Anne, 2021. "Feasibility-free axiomatization of the core and its non-empty extension," Economics Letters, Elsevier, vol. 201(C).
    21. Yan-An Hwang, 2013. "On the core: complement-reduced game and max-reduced game," International Journal of Game Theory, Springer;Game Theory Society, vol. 42(2), pages 339-355, May.

    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:gam:jmathe:v:11:y:2023:i:13:p:2812-:d:1177158. 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: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.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.