IDEAS home Printed from https://ideas.repec.org/a/spr/jogath/v45y2016i4d10.1007_s00182-015-0500-z.html
   My bibliography  Save this article

A monotonic core solution for convex TU games

Author

Listed:
  • J. Arin

    (University of the Basque Country)

  • I. Katsev

    (St Petersburg Institute for Economics and Mathematics)

Abstract

We find that the answer to the open question of whether there is a continuous core solution that satisfies coalitional monotonicity in the class of convex games is yes. We prove that the SD-prenucleolus is a continuous core solution that satisfies coalitional monotonicity for convex games, a class of games widely used to model economic situations.

Suggested Citation

  • J. Arin & I. Katsev, 2016. "A monotonic core solution for convex TU games," International Journal of Game Theory, Springer;Game Theory Society, vol. 45(4), pages 1013-1029, November.
    • Handle: RePEc:spr:jogath:v:45:y:2016:i:4:d:10.1007_s00182-015-0500-z
    DOI: 10.1007/s00182-015-0500-z
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s00182-015-0500-z
    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/s00182-015-0500-z?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. Dutta, Bhaskar & Ray, Debraj, 1989. "A Concept of Egalitarianism under Participation Constraints," Econometrica, Econometric Society, vol. 57(3), pages 615-635, May.
    2. J. Arin & I. Katsev, 2014. "The SD-prenucleolus for TU games," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 80(3), pages 307-327, December.
    3. J. Arin, 2013. "Monotonic core solutions: beyond Young’s theorem," International Journal of Game Theory, Springer;Game Theory Society, vol. 42(2), pages 325-337, May.
    4. Katsev, Ilya & Arin Aguirre, Francisco Javier, 2011. "The SD-prenucleolus for TU games," IKERLANAK 2011-56, Universidad del País Vasco - Departamento de Fundamentos del Análisis Económico I.
    5. SCHMEIDLER, David, 1969. "The nucleolus of a characteristic function game," LIDAM Reprints CORE 44, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    6. Toru Hokari, 2000. "note: The nucleolus is not aggregate-monotonic on the domain of convex games," International Journal of Game Theory, Springer;Game Theory Society, vol. 29(1), pages 133-137.
    7. 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, March.
    8. Kleppe, J., 2010. "Modelling interactive behaviour, and solution concepts," Other publications TiSEM b9b96884-5761-48f0-9ee4-4, Tilburg University, School of Economics and Management.
    9. Arin, Javier & Inarra, Elena, 1998. "A Characterization of the Nucleolus for Convex Games," Games and Economic Behavior, Elsevier, vol. 23(1), pages 12-24, April.
    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. Arin Aguirre, Francisco Javier & Katsev, Ilya, 2016. "The SD-prekernel for TU games," IKERLANAK info:eu-repo/grantAgreeme, Universidad del País Vasco - Departamento de Fundamentos del Análisis Económico I.

    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. Arin Aguirre, Francisco Javier & Katsev, Ilya, 2016. "The SD-prekernel for TU games," IKERLANAK info:eu-repo/grantAgreeme, Universidad del País Vasco - Departamento de Fundamentos del Análisis Económico I.
    2. Calleja, Pedro & Llerena, Francesc & Sudhölter, Peter, 2021. "Axiomatizations of Dutta-Ray’s egalitarian solution on the domain of convex games," Journal of Mathematical Economics, Elsevier, vol. 95(C).
    3. 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.
    4. Calleja, Pere & Llerena Garrés, Francesc, 2015. "On the (in)compatibility of rationality, monotonicity and consistency for cooperative games," Working Papers 2072/247807, Universitat Rovira i Virgili, Department of Economics.
    5. Peter Knudsen & Lars Østerdal, 2012. "Merging and splitting in cooperative games: some (im)possibility results," International Journal of Game Theory, Springer;Game Theory Society, vol. 41(4), pages 763-774, November.
    6. Arin Aguirre, Francisco Javier & Katsev, Ilya, 2011. "The SD-prenucleolus for TU games," IKERLANAK info:eu-repo/grantAgreeme, Universidad del País Vasco - Departamento de Fundamentos del Análisis Económico I.
    7. Pedro Calleja & Francesc Llerena, 2017. "Rationality, aggregate monotonicity and consistency in cooperative games: some (im)possibility results," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 48(1), pages 197-220, January.
    8. Hougaard, Jens Leth & Østerdal, Lars Peter, 2010. "Monotonicity of social welfare optima," Games and Economic Behavior, Elsevier, vol. 70(2), pages 392-402, November.
    9. John Kleppe & Hans Reijnierse & Peter Sudhölter, 2016. "Axiomatizations of symmetrically weighted solutions," Annals of Operations Research, Springer, vol. 243(1), pages 37-53, August.
    10. Dietzenbacher, Bas, 2020. "Monotonicity and Egalitarianism (revision of CentER DP 2019-007)," Other publications TiSEM 295f156e-91ad-4177-b61a-1, Tilburg University, School of Economics and Management.
    11. Moshe Babaioff & Uriel Feige, 2019. "A New Approach to Fair Distribution of Welfare," Papers 1909.11346, arXiv.org.
    12. 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.
    13. Calleja, Pedro & Llerena, Francesc, 2020. "Consistency, weak fairness, and the Shapley value," Mathematical Social Sciences, Elsevier, vol. 105(C), pages 28-33.
    14. Dietzenbacher, Bas, 2021. "Monotonicity and egalitarianism," Games and Economic Behavior, Elsevier, vol. 127(C), pages 194-205.
    15. Le Breton, Michel & Montero, Maria & Zaporozhets, Vera, 2012. "Voting power in the EU council of ministers and fair decision making in distributive politics," Mathematical Social Sciences, Elsevier, vol. 63(2), pages 159-173.
    16. 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.
    17. Llerena, Francesc & Mauri, Llúcia, 2017. "On the existence of the Dutta–Ray’s egalitarian solution," Mathematical Social Sciences, Elsevier, vol. 89(C), pages 92-99.
    18. Klijn, F. & Slikker, M. & Tijs, S.H. & Zarzuelo, J., 1998. "Characterizations of the Egalitarian Solution for Convex Games," Other publications TiSEM 0a127ca4-b1ae-47e7-a135-3, Tilburg University, School of Economics and Management.
    19. Hougaard, Jens Leth & Smilgins, Aleksandrs, 2016. "Risk capital allocation with autonomous subunits: The Lorenz set," Insurance: Mathematics and Economics, Elsevier, vol. 67(C), pages 151-157.
    20. Guni Orshan & Peter Sudhölter, 2012. "Nonsymmetric variants of the prekernel and the prenucleolus," International Journal of Game Theory, Springer;Game Theory Society, vol. 41(4), pages 809-828, November.

    More about this item

    Keywords

    Convex games; Prenucleolus; Core; Monotonicity;
    All these keywords.

    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games

    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:jogath:v:45:y:2016:i:4:d:10.1007_s00182-015-0500-z. 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.