IDEAS home Printed from https://ideas.repec.org/a/spr/etbull/v10y2022i1d10.1007_s40505-022-00223-5.html
   My bibliography  Save this article

Existence of alpha-core allocations in economies with non-ordered and discontinuous preferences

Author

Listed:
  • Vincenzo Scalzo

    (University of Napoli Federico II via Cinthia (Monte S. Angelo))

Abstract

We study exchange economies where the preference relation of each consumer depends also on the consumptions of the other consumers. In the setting of economies with a finite number $$n\ge 2$$ n ≥ 2 of consumers and non-ordered and discontinuous preferences, we give sufficient and necessary conditions for the existence of alpha-core allocations in the sense of Yannelis (Equilibrium theory in infinite dimensional spaces, 102–123, 1991). The result has been obtained by means of the Ky Fan minimax inequality.

Suggested Citation

  • Vincenzo Scalzo, 2022. "Existence of alpha-core allocations in economies with non-ordered and discontinuous preferences," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 10(1), pages 1-12, May.
    • Handle: RePEc:spr:etbull:v:10:y:2022:i:1:d:10.1007_s40505-022-00223-5
    DOI: 10.1007/s40505-022-00223-5
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s40505-022-00223-5
    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/s40505-022-00223-5?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. 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. Efe A. Ok & Levent KoÚkesen, 2000. "Negatively interdependent preferences," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 17(3), pages 533-558.
    3. Kockesen, Levent & Ok, Efe A. & Sethi, Rajiv, 2000. "The Strategic Advantage of Negatively Interdependent Preferences," Journal of Economic Theory, Elsevier, vol. 92(2), pages 274-299, June.
    4. Scalzo, Vincenzo, 2019. "Equilibrium existence in games: Slight single deviation property and Ky Fan minimax inequality," Journal of Mathematical Economics, Elsevier, vol. 82(C), pages 197-201.
    5. Scarf, Herbert E., 1971. "On the existence of a coopertive solution for a general class of N-person games," Journal of Economic Theory, Elsevier, vol. 3(2), pages 169-181, June.
    6. Philip J. Reny, 2020. "Nash Equilibrium in Discontinuous Games," Annual Review of Economics, Annual Reviews, vol. 12(1), pages 439-470, August.
    7. Vincenzo Scalzo, 2013. "Essential equilibria of discontinuous games," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 54(1), pages 27-44, September.
    8. Stanley Reiter, 2001. "Interdependent Preferences and Groups of Agents," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 3(1), pages 27-67, January.
    9. Holly, Charles, 1994. "An Exchange Economy Can Have an Empty Alpha-Core," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 4(3), pages 453-461, May.
    10. Guoqiang Tian, 1993. "Necessary and Sufficient Conditions for Maximization of a Class of Preference Relations," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 60(4), pages 949-958.
    11. Rabia Nessah & Guoqiang Tian, 2016. "On the existence of Nash equilibrium in discontinuous games," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 61(3), pages 515-540, March.
    12. Guoqiang Tian & Liyan Yang, 2009. "Theory of negative consumption externalities with applications to the economics of happiness," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 39(3), pages 399-424, June.
    13. Drakopoulos, Stavros A., 2012. "The History Of Attitudes Towards Interdependent Preferences," Journal of the History of Economic Thought, Cambridge University Press, vol. 34(4), pages 541-557, December.
    14. Michael R. Baye & Guoqiang Tian & Jianxin Zhou, 1993. "Characterizations of the Existence of Equilibria in Games with Discontinuous and Non-quasiconcave Payoffs," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 60(4), pages 935-948.
    15. Bill Dupor & Wen-Fang Liu, 2003. "Jealousy and Equilibrium Overconsumption," American Economic Review, American Economic Association, vol. 93(1), pages 423-428, March.
    16. Border, Kim C, 1984. "A Core Existence Theorem for Games without Ordered Preferences," Econometrica, Econometric Society, vol. 52(6), pages 1537-1542, November.
    17. Zhao, Jingang, 1996. "The hybrid equilibria and core selection in exchange economies with externalities," Journal of Mathematical Economics, Elsevier, vol. 26(4), pages 387-407.
    18. Borglin, Anders, 1973. "Price characterization of stable allocations in exchange economies with externalities," Journal of Economic Theory, Elsevier, vol. 6(5), pages 483-494, October.
    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. Maria Gabriella Graziano & Claudia Meo & Nicholas C. Yannelis, 2023. "Core and stable sets of exchange economies with externalities," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 11(1), pages 27-44, April.
    2. Ken Urai & Hiromi Murakami & Weiye Chen, 2023. "Generalization of the social coalitional equilibrium structure," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 11(1), pages 1-25, April.

    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. Scalzo, Vincenzo, 2020. "Doubly Strong Equilibrium," MPRA Paper 99329, University Library of Munich, Germany.
    2. Maria Gabriella Graziano & Claudia Meo & Nicholas C. Yannelis, 2023. "Core and stable sets of exchange economies with externalities," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 11(1), pages 27-44, April.
    3. 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.
    4. Scalzo, Vincenzo, 2023. "Existence and stability results on the unilateral support equilibrium," Mathematical Social Sciences, Elsevier, vol. 123(C), pages 1-9.
    5. 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.
    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. Christian Pietro & Maria Gabriella Graziano & Vincenzo Platino, 2022. "Social loss with respect to the core of an economy with externalities," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 73(2), pages 487-508, April.
    8. Martins-da-Rocha, Victor Filipe & Yannelis, Nicholas C., 2011. "Non-emptiness of the alpha-core," FGV EPGE Economics Working Papers (Ensaios Economicos da EPGE) 716, EPGE Brazilian School of Economics and Finance - FGV EPGE (Brazil).
    9. 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).
    10. 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.
    11. Nessah, Rabia & Tian, Guoqiang, 2008. "Existence of Equilibria in Discontinuous Games," MPRA Paper 41206, University Library of Munich, Germany, revised Mar 2010.
    12. M. Ali Khan & Metin Uyanik, 2021. "The Yannelis–Prabhakar theorem on upper semi-continuous selections in paracompact spaces: extensions and applications," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 71(3), pages 799-840, April.
    13. Tieying Huang & Jiuqiang Liu, 2022. "Fuzzy Strong Nash Equilibria in Generalized Fuzzy Games with Application in Urban Public-Sports Services," Mathematics, MDPI, vol. 10(20), pages 1-10, October.
    14. Rabia Nessah & Raluca Parvulescu, 2017. "On the Existence of Pareto Efficient Nash Equilibria in Discontinuous Games," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 19(03), pages 1-13, September.
    15. Rabia Nessah, 2022. "Weakly continuous security and nash equilibrium," Theory and Decision, Springer, vol. 93(4), pages 725-745, November.
    16. Khan, M. Ali & McLean, Richard P. & Uyanik, Metin, 2024. "On constrained generalized games with action sets in non-locally-convex and non-Hausdorff topological vector spaces," Journal of Mathematical Economics, Elsevier, vol. 111(C).
    17. 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.
    18. Alger, Ingela, 2021. "On the evolution of male competitiveness," Journal of Economic Behavior & Organization, Elsevier, vol. 190(C), pages 228-254.
    19. Ingela Alger & Jörgen W. Weibull, 2013. "Homo Moralis—Preference Evolution Under Incomplete Information and Assortative Matching," Econometrica, Econometric Society, vol. 81(6), pages 2269-2302, November.
    20. repec:tiu:tiutis:fe79a9d2-e9e3-4dbc-9539-cdece886993d is not listed on IDEAS
    21. Natalia Lazzati, 2013. "Comparison of equilibrium actions and payoffs across players in games of strategic complements," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 54(3), pages 777-788, November.

    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:etbull:v:10:y:2022:i:1:d:10.1007_s40505-022-00223-5. 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.