IDEAS home Printed from https://ideas.repec.org/p/bge/wpaper/327.html
   My bibliography  Save this paper

A simple procedure for computing strong constrained egalitarian allocations

Author

Listed:
  • Francesc Llerena
  • Carles Rafels
  • Cori Vilella

Abstract

This paper deals with the strong constrained egalitarian solution introduced by Dutta and Ray (1991). We show that this solution yields the weak constrained egalitarian allocations (Dutta and Ray, 1989) associated to a finite family of convex games. This relationship makes it possible to define a systematic way of computing the strong constrained egalitarian allocations for any arbitrary game, using the well-known Dutta-Rayís algorithm for convex games. We also characterize non-emptiness and show that the set of strong constrained egalitarian allocations Lorenz dominates every other point in the equal division core (Selten, 1972).

Suggested Citation

  • Francesc Llerena & Carles Rafels & Cori Vilella, 2008. "A simple procedure for computing strong constrained egalitarian allocations," Working Papers 327, Barcelona School of Economics.
    • Handle: RePEc:bge:wpaper:327
    as

    Download full text from publisher

    File URL: http://www.barcelonagse.eu/sites/default/files/working_paper_pdfs/327.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Anindya Bhattacharya, 2004. "On the equal division core," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 22(2), pages 391-399, April.
    2. Toru Hokari, 2000. "Population monotonic solutions on convex games," International Journal of Game Theory, Springer;Game Theory Society, vol. 29(3), pages 327-338.
    3. Dutta, Bhaskar & Ray, Debraj, 1989. "A Concept of Egalitarianism under Participation Constraints," Econometrica, Econometric Society, vol. 57(3), pages 615-635, May.
    4. Dutta, Bhaskar & Ray, Debraj, 1991. "Constrained egalitarian allocations," Games and Economic Behavior, Elsevier, vol. 3(4), pages 403-422, November.
    5. Arin, Javier & Kuipers, Jeroen & Vermeulen, Dries, 2003. "Some characterizations of egalitarian solutions on classes of TU-games," Mathematical Social Sciences, Elsevier, vol. 46(3), pages 327-345, December.
    6. Klijn, Flip & Slikker, Marco & Tijs, Stef & Zarzuelo, Jose, 2000. "The egalitarian solution for convex games: some characterizations," Mathematical Social Sciences, Elsevier, vol. 40(1), pages 111-121, July.
    7. Jens Leth Hougaard & Lars Thorlund-Petersen & Bezalel Peleg, 2001. "On the set of Lorenz-maximal imputations in the core of a balanced game," International Journal of Game Theory, Springer;Game Theory Society, vol. 30(2), pages 147-165.
    8. Dutta, B, 1990. "The Egalitarian Solution and Reduced Game Properties in Convex Games," International Journal of Game Theory, Springer;Game Theory Society, vol. 19(2), pages 153-169.
    9. Javier Arin & Elena Inarra, 2001. "Egalitarian solutions in the core," International Journal of Game Theory, Springer;Game Theory Society, vol. 30(2), pages 187-193.
    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. Vincent Iehlé, 2015. "The lattice structure of the S-Lorenz core," Theory and Decision, Springer, vol. 78(1), pages 141-151, January.
    2. Francesc Llerena & Cori Vilella, 2015. "The equity core and the Lorenz-maximal allocations in the equal division core," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 81(2), pages 235-244, 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. Dietzenbacher, Bas, 2019. "The Procedural Egalitarian Solution and Egalitarian Stable Games," Other publications TiSEM 6caea8c0-1dcd-4038-88da-b, Tilburg University, School of Economics and Management.
    2. Brânzei, R. & Llorca, N. & Sánchez-Soriano, J. & Tijs, S.H., 2007. "Egalitarianism in Multi-Choice Games," Discussion Paper 2007-55, Tilburg University, Center for Economic Research.
    3. Brânzei, R. & Llorca, N. & Sánchez-Soriano, J. & Tijs, S.H., 2007. "Egalitarianism in Multi-Choice Games," Other publications TiSEM bfbd67a5-701f-4be7-a1c9-0, Tilburg University, School of Economics and Management.
    4. Branzei, Rodica & Dimitrov, Dinko & Tijs, Stef, 2004. "Egalitarianism in convex fuzzy games," Mathematical Social Sciences, Elsevier, vol. 47(3), pages 313-325, May.
    5. Dietzenbacher, Bas & Yanovskaya, Elena, 2020. "Antiduality in exact partition games," Mathematical Social Sciences, Elsevier, vol. 108(C), pages 116-121.
    6. 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.
    7. Dietzenbacher, Bas & Dogan, Emre, 2024. "Population monotonicity and egalitarianism," Research Memorandum 007, Maastricht University, Graduate School of Business and Economics (GSBE).
    8. Takafumi Otsuka, 2020. "Egalitarian solution for games with discrete side payment," Papers 2003.10059, arXiv.org.
    9. Dietzenbacher, Bas, 2021. "Monotonicity and egalitarianism," Games and Economic Behavior, Elsevier, vol. 127(C), pages 194-205.
    10. Hougaard, Jens Leth & Østerdal, Lars Peter, 2010. "Monotonicity of social welfare optima," Games and Economic Behavior, Elsevier, vol. 70(2), pages 392-402, November.
    11. 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.
    12. 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).
    13. Francesc Llerena & Cori Vilella, 2013. "An axiomatic characterization of the strong constrained egalitarian solution," Economics Bulletin, AccessEcon, vol. 33(2), pages 1438-1445.
    14. Francesc Llerena & Llúcia Mauri, 2016. "Reduced games and egalitarian solutions," International Journal of Game Theory, Springer;Game Theory Society, vol. 45(4), pages 1053-1069, November.
    15. Llerena Garrés, Francesc & Mauri Masdeu, Llúcia, 2014. "On reduced games and the lexmax solution," Working Papers 2072/237591, Universitat Rovira i Virgili, Department of Economics.
    16. Llerena Garrés, Francesc & Mauri Masdeu, Llúcia, 2016. "On the existence of the Dutta-Ray’s egalitarian solution," Working Papers 2072/266573, Universitat Rovira i Virgili, Department of Economics.
    17. Calleja, Pedro & Llerena, Francesc & Sudhölter, Peter, 2019. "Welfare egalitarianism in surplus-sharing problems and convex games," Discussion Papers on Economics 6/2019, University of Southern Denmark, Department of Economics.
    18. Takanashi, Seiji, 2024. "Analysis of the core under inequality-averse utility functions," Mathematical Social Sciences, Elsevier, vol. 129(C), pages 52-60.
    19. Dietzenbacher, Bas & Borm, Peter & Hendrickx, Ruud, 2017. "The procedural egalitarian solution," Games and Economic Behavior, Elsevier, vol. 106(C), pages 179-187.
    20. 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.

    More about this item

    Keywords

    Cooperative TU-game; Strong Constrained Egalitarian Solution; Weak Constrained Egalitarian Solution; Equal Division Core; Lorenz Domination;
    All these keywords.

    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
    • C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory

    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:bge:wpaper:327. 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: Bruno Guallar (email available below). General contact details of provider: https://edirc.repec.org/data/bargses.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.