IDEAS home Printed from https://ideas.repec.org/p/man/sespap/1105.html
   My bibliography  Save this paper

Nonemptiness of the alpha-core

Author

Listed:
  • V. Filipe Martins-da-Rocha
  • Nicholas C. Yannelis

Abstract

We prove non-emptiness of the alpha-core for balanced games with non-ordered preferences, extending and generalizing in several aspects the results of Scarf (1971), Border (1984), Florenzano (1989), Yannelis (1991) and Kajii (1992). In particular we answer an open question in Kajii (1992) regarding the applicability of the non-emptiness results to models with infinite dimensional strategy spaces. We provide two models with Knightian and voting preferences for which the results of Scarf (1971) and Kajii (1992) cannot be applied while our non-emptiness result applies.
(This abstract was borrowed from another version of this item.)

Suggested Citation

  • V. Filipe Martins-da-Rocha & Nicholas C. Yannelis, 2011. "Nonemptiness of the alpha-core," Economics Discussion Paper Series 1105, Economics, The University of Manchester.
    • Handle: RePEc:man:sespap:1105
    as

    Download full text from publisher

    File URL: http://hummedia.manchester.ac.uk/schools/soss/economics/discussionpapers/EDP-1105.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. 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.
    2. Rigotti, Luca & Shannon, Chris, 2001. "Uncertainty and Risk in Financial Markets," Department of Economics, Working Paper Series qt7pp7113z, Department of Economics, Institute for Business and Economic Research, UC Berkeley.
    3. Bonnisseau, Jean-Marc & Iehle, Vincent, 2007. "Payoff-dependent balancedness and cores," Games and Economic Behavior, Elsevier, vol. 61(1), pages 1-26, October.
    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. Luca Rigotti & Chris Shannon, 2005. "Uncertainty and Risk in Financial Markets," Econometrica, Econometric Society, vol. 73(1), pages 203-243, January.
    6. Border, Kim C, 1984. "A Core Existence Theorem for Games without Ordered Preferences," Econometrica, Econometric Society, vol. 52(6), pages 1537-1542, November.
    7. Florenzano Monique, 1987. "On the non-emptiness of the core of a coalitional production economy without ordered preferences," CEPREMAP Working Papers (Couverture Orange) 8733, CEPREMAP.
    8. repec:dau:papers:123456789/89 is not listed on IDEAS
    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. Podczeck, Konrad & Yannelis, Nicholas C., 2008. "Equilibrium theory with asymmetric information and with infinitely many commodities," Journal of Economic Theory, Elsevier, vol. 141(1), pages 152-183, July.
    11. Koutsougeras, Leonidas C & Yannelis, Nicholas C, 1993. "Incentive Compatibility and Information Superiority of the Core of an Economy with Differential Information," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 3(2), pages 195-216, April.
    12. Isabelle Lefebvre, 2001. "An alternative proof of the nonemptiness of the private core," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 18(2), pages 275-291.
    13. Mas-Colell, Andreu & Zame, William R., 1991. "Equilibrium theory in infinite dimensional spaces," Handbook of Mathematical Economics, in: W. Hildenbrand & H. Sonnenschein (ed.), Handbook of Mathematical Economics, edition 1, volume 4, chapter 34, pages 1835-1898, Elsevier.
    14. 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).
    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. Askoura, Y. & Sbihi, M. & Tikobaini, H., 2013. "The ex ante α-core for normal form games with uncertainty," Journal of Mathematical Economics, Elsevier, vol. 49(2), pages 157-162.
    2. Graziano, Maria Gabriella & Meo, Claudia & Yannelis, Nicholas C., 2017. "Stable sets for exchange economies with interdependent preferences," Journal of Economic Behavior & Organization, Elsevier, vol. 140(C), pages 267-286.
    3. 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.
    4. Uyanık, Metin, 2015. "On the nonemptiness of the α-core of discontinuous games: Transferable and nontransferable utilities," Journal of Economic Theory, Elsevier, vol. 158(PA), pages 213-231.
    5. 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.
    6. 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.

    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 & 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.
    2. 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).
    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. Bonnisseau, Jean-Marc & Iehle, Vincent, 2007. "Payoff-dependent balancedness and cores," Games and Economic Behavior, Elsevier, vol. 61(1), pages 1-26, October.
    5. Liu, Jiuqiang & Liu, Xiaodong, 2013. "A necessary and sufficient condition for an NTU fuzzy game to have a non-empty fuzzy core," Journal of Mathematical Economics, Elsevier, vol. 49(2), pages 150-156.
    6. Iehle, Vincent, 2007. "The core-partition of a hedonic game," Mathematical Social Sciences, Elsevier, vol. 54(2), pages 176-185, September.
    7. repec:dau:papers:123456789/89 is not listed on IDEAS
    8. 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.
    9. 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.
    10. Claudia Meo, 2015. "Cooperative Solutions for Large Economies with Asymmetric Information," Metroeconomica, Wiley Blackwell, vol. 66(1), pages 71-90, February.
    11. Nizar Allouch & Myrna Wooders, 2017. "On the nonemptiness of approximate cores of large games," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 63(1), pages 191-209, January.
    12. Tian, Dejian & Tian, Weidong, 2014. "Optimal risk-sharing under mutually singular beliefs," Mathematical Social Sciences, Elsevier, vol. 72(C), pages 41-49.
    13. Patrick Beissner & Frank Riedel, 2018. "Non-implementability of Arrow–Debreu equilibria by continuous trading under volatility uncertainty," Finance and Stochastics, Springer, vol. 22(3), pages 603-620, July.
    14. 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).
    15. 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.
    16. Król, Michał, 2012. "Product differentiation decisions under ambiguous consumer demand and pessimistic expectations," International Journal of Industrial Organization, Elsevier, vol. 30(6), pages 593-604.
    17. 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.
    18. He, Wei & Yannelis, Nicholas C., 2015. "Equilibrium theory under ambiguity," Journal of Mathematical Economics, Elsevier, vol. 61(C), pages 86-95.
    19. repec:ipg:wpaper:2014-061 is not listed on IDEAS
    20. Basile, Achille & Graziano, Maria Gabriella & Papadaki, Maria & Polyrakis, Ioannis A., 2017. "Cones with semi-interior points and equilibrium," Journal of Mathematical Economics, Elsevier, vol. 71(C), pages 36-48.
    21. Charalambos Aliprantis & Kim Border & Owen Burkinshaw, 1996. "Market economies with many commodities," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 19(1), pages 113-185, March.
    22. Luciano I. de Castro & Marialaura Pesce & Nicholas C. Yannelis, 2013. "A New Perspective on Rational Expectations," Economics Discussion Paper Series 1316, Economics, The University of Manchester.

    More about this item

    NEP fields

    This paper has been announced in the following NEP Reports:

    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:man:sespap:1105. 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: Marianne Sensier (email available below). General contact details of provider: https://edirc.repec.org/data/semanuk.html .

    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.