IDEAS home Printed from https://ideas.repec.org/a/spr/annopr/v336y2024i3d10.1007_s10479-022-05090-8.html
   My bibliography  Save this article

On the $$\alpha $$ α -core of set payoffs games

Author

Listed:
  • Yu Zhang

    (Yunnan University of Finance and Economics)

  • Xiangkai Sun

    (Chongqing Technology and Business University)

Abstract

This paper deals with $$\alpha $$ α -core of set payoffs games with finitely many players and finite coalition $$\alpha $$ α -core of set payoffs games with infinitely many players. We present an existence theorem of $$\alpha $$ α -core of set payoffs games with finitely many players. By virtue of finite intersection property, we also establish an existence theorem of finite coalition $$\alpha $$ α -core of set payoffs games with infinitely many players. Besides, we obtain some stability results of solution mapping of $$\alpha $$ α -core of set payoffs games, where set payoff functions and action sets of agents involve perturbed parameters. Moreover, as applications, we obtain the corresponding results for $$\alpha $$ α -core of vector payoffs games.

Suggested Citation

  • Yu Zhang & Xiangkai Sun, 2024. "On the $$\alpha $$ α -core of set payoffs games," Annals of Operations Research, Springer, vol. 336(3), pages 1505-1518, May.
    • Handle: RePEc:spr:annopr:v:336:y:2024:i:3:d:10.1007_s10479-022-05090-8
    DOI: 10.1007/s10479-022-05090-8
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10479-022-05090-8
    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/s10479-022-05090-8?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 search for a different version of it.

    References listed on IDEAS

    as
    1. S.J. Li & G.Y. Chen & K.L. Teo, 2002. "On the Stability of Generalized Vector Quasivariational Inequality Problems," Journal of Optimization Theory and Applications, Springer, vol. 113(2), pages 283-295, May.
    2. Askoura, Y., 2015. "An interim core for normal form games and exchange economies with incomplete information," Journal of Mathematical Economics, Elsevier, vol. 58(C), pages 38-45.
    3. Y. Askoura, 2015. "An interim core for normal form games and exchange economies with incomplete information," Post-Print hal-04149208, HAL.
    4. Weber, S., 1981. "Some results on the weak core of a non-side-payment game with infinitely many players," Journal of Mathematical Economics, Elsevier, vol. 8(1), pages 101-111, March.
    5. Yang, Zhe, 2018. "Some generalizations of Kajii’s theorem to games with infinitely many players," Journal of Mathematical Economics, Elsevier, vol. 76(C), pages 131-135.
    6. Ichiishi, Tatsuro, 1981. "A Social Coalitional Equilibrium Existence Lemma," Econometrica, Econometric Society, vol. 49(2), pages 369-377, March.
    7. Askoura, Y., 2017. "On the core of normal form games with a continuum of players," Mathematical Social Sciences, Elsevier, vol. 89(C), pages 32-42.
    8. Noguchi, Mitsunori, 2018. "Alpha cores of games with nonatomic asymmetric information," Journal of Mathematical Economics, Elsevier, vol. 75(C), pages 1-12.
    9. Kajii, Atsushi, 1992. "A generalization of Scarf's theorem: An [alpha]-core existence theorem without transitivity or completeness," Journal of Economic Theory, Elsevier, vol. 56(1), pages 194-205, February.
    10. Noguchi, Mitsunori, 2014. "Cooperative equilibria of finite games with incomplete information," Journal of Mathematical Economics, Elsevier, vol. 55(C), pages 4-10.
    11. Zhe Yang & Yan Ju, 2016. "Existence and generic stability of cooperative equilibria for multi-leader-multi-follower games," Journal of Global Optimization, Springer, vol. 65(3), pages 563-573, July.
    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. Yang, Zhe & Zhang, Xian, 2021. "A weak α-core existence theorem of games with nonordered preferences and a continuum of agents," Journal of Mathematical Economics, Elsevier, vol. 94(C).
    2. Yang, Zhe & Yuan, George Xianzhi, 2019. "Some generalizations of Zhao’s theorem: Hybrid solutions and weak hybrid solutions for games with nonordered preferences," Journal of Mathematical Economics, Elsevier, vol. 84(C), pages 94-100.
    3. 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.
    4. Zhe Yang & Haiqun Zhang, 2019. "NTU core, TU core and strong equilibria of coalitional population games with infinitely many pure strategies," Theory and Decision, Springer, vol. 87(2), pages 155-170, September.
    5. Yang, Zhe, 2020. "The weak α-core of exchange economies with a continuum of players and pseudo-utilities," Journal of Mathematical Economics, Elsevier, vol. 91(C), pages 43-50.
    6. Yang, Zhe & Song, Qingping, 2022. "A weak α-core existence theorem of generalized games with infinitely many players and pseudo-utilities," Mathematical Social Sciences, Elsevier, vol. 116(C), pages 40-46.
    7. Yang, Zhe, 2018. "Some generalizations of Kajii’s theorem to games with infinitely many players," Journal of Mathematical Economics, Elsevier, vol. 76(C), pages 131-135.
    8. Yang, Zhe, 2017. "Some infinite-player generalizations of Scarf’s theorem: Finite-coalition α-cores and weak α-cores," Journal of Mathematical Economics, Elsevier, vol. 73(C), pages 81-85.
    9. Crettez, Bertrand & Nessah, Rabia & Tazdaït, Tarik, 2022. "On the strong hybrid solution of an n-person game," Mathematical Social Sciences, Elsevier, vol. 117(C), pages 61-68.
    10. Lan Di & George X. Yuan & Tu Zeng, 2021. "The consensus equilibria of mining gap games related to the stability of Blockchain Ecosystems," The European Journal of Finance, Taylor & Francis Journals, vol. 27(4-5), pages 419-440, March.
    11. Askoura, Y., 2017. "On the core of normal form games with a continuum of players," Mathematical Social Sciences, Elsevier, vol. 89(C), pages 32-42.
    12. Bonnisseau, Jean-Marc & Iehle, Vincent, 2007. "Payoff-dependent balancedness and cores," Games and Economic Behavior, Elsevier, vol. 61(1), pages 1-26, October.
    13. Scalzo, Vincenzo, 2020. "Doubly Strong Equilibrium," MPRA Paper 99329, University Library of Munich, Germany.
    14. Youcef Askoura, 2019. "On the core of normal form games with a continuum of players : a correction," Papers 1903.09819, arXiv.org.
    15. Jean-Marc Bonnisseau & Vincent Iehlé, 2007. "Payoff-dependent balancedness and cores (revised version)," UFAE and IAE Working Papers 678.07, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC).
    16. Youcef Askoura, 2019. "An interim core for normal form games and exchange economies with incomplete information: a correction," Papers 1903.09867, arXiv.org.
    17. Noguchi, Mitsunori, 2021. "Essential stability of the alpha cores of finite games with incomplete information," Mathematical Social Sciences, Elsevier, vol. 110(C), pages 34-43.
    18. Ren-you Zhong & Nan-jing Huang, 2011. "Lower Semicontinuity for Parametric Weak Vector Variational Inequalities in Reflexive Banach Spaces," Journal of Optimization Theory and Applications, Springer, vol. 150(2), pages 317-326, August.
    19. Ichiishi, Tatsuro, 1985. "Management versus ownership, II," European Economic Review, Elsevier, vol. 27(2), pages 115-138, March.
    20. Lam Anh & Phan Khanh, 2010. "Continuity of solution maps of parametric quasiequilibrium problems," Journal of Global Optimization, Springer, vol. 46(2), pages 247-259, February.

    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:336:y:2024:i:3:d:10.1007_s10479-022-05090-8. 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.