IDEAS home Printed from https://ideas.repec.org/p/hig/wpaper/85-ec-2014.html
   My bibliography  Save this paper

Self-Covariant Solutions To Cooperative Games With Transferable Utilities

Author

Listed:
  • Elena B.Yanovskaya

    (National Research University Higher School of Economics)

Abstract

A weakening of covariance property for solutions of cooperative games with transferable utilities self-covariance is dened. Self-covariant solutions are positively homogenous and satisfy a "restricted"translation covariance such that feasible shifts are only the solution vectors themselves and their multipliers. A description of all nonempty, ecient, anonymous, self-covariant, and single-valued solution for the class of two-person TU games is given. Among them the solutions admitting consistent extensions in the DavisMaschler sense are found. They are the equal share solution, the standard solution, and the constrained egalitarian solution for superadditive twoperson games. Characterizations of consistent extensions (Thomson 1996) of these solutions to the class of all TU games are given.

Suggested Citation

  • Elena B.Yanovskaya, 2014. "Self-Covariant Solutions To Cooperative Games With Transferable Utilities," HSE Working papers WP BRP 85/EC/2014, National Research University Higher School of Economics.
    • Handle: RePEc:hig:wpaper:85/ec/2014
    as

    Download full text from publisher

    File URL: http://www.hse.ru/data/2014/12/16/1103403985/85EC2014.pdf
    Download Restriction: no
    ---><---

    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. Hart, Sergiu & Mas-Colell, Andreu, 1989. "Potential, Value, and Consistency," Econometrica, Econometric Society, vol. 57(3), pages 589-614, May.
    3. 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.
    4. Peleg, B, 1986. "On the Reduced Game Property and Its Converse," International Journal of Game Theory, Springer;Game Theory Society, vol. 15(3), pages 187-200.
    5. Thomson, W., 1996. "Consistent Allocation Rules," RCER Working Papers 418, University of Rochester - Center for Economic Research (RCER).
    6. 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.
    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. Elena Yanovskaya, 2016. "An Extension of a Class of Cost Sharing Methods to the Solutions of the Class of Two-Person Cooperative Games," HSE Working papers WP BRP 127/EC/2016, National Research University Higher School of Economics.

    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. 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.
    2. 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.
    3. Dietzenbacher, Bas & Yanovskaya, Elena, 2020. "Antiduality in exact partition games," Mathematical Social Sciences, Elsevier, vol. 108(C), pages 116-121.
    4. 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).
    5. Bas Dietzenbacher & Peter Sudhölter, 2022. "Hart–Mas-Colell consistency and the core in convex games," International Journal of Game Theory, Springer;Game Theory Society, vol. 51(2), pages 413-429, June.
    6. Takafumi Otsuka, 2020. "Egalitarian solution for games with discrete side payment," Papers 2003.10059, arXiv.org.
    7. Francesc Llerena & Cori Vilella, 2013. "An axiomatic characterization of the strong constrained egalitarian solution," Economics Bulletin, AccessEcon, vol. 33(2), pages 1438-1445.
    8. 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.
    9. 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.
    10. 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.
    11. Oishi, Takayuki & Nakayama, Mikio & Hokari, Toru & Funaki, Yukihiko, 2016. "Duality and anti-duality in TU games applied to solutions, axioms, and axiomatizations," Journal of Mathematical Economics, Elsevier, vol. 63(C), pages 44-53.
    12. 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.
    13. William Thomson, 2011. "Consistency and its converse: an introduction," Review of Economic Design, Springer;Society for Economic Design, vol. 15(4), pages 257-291, December.
    14. Branzei, Rodica & Dimitrov, Dinko & Tijs, Stef, 2004. "Egalitarianism in convex fuzzy games," Mathematical Social Sciences, Elsevier, vol. 47(3), pages 313-325, May.
    15. 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.
    16. 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.
    17. 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.
    18. Dietzenbacher, Bas & Borm, Peter & Hendrickx, Ruud, 2017. "The procedural egalitarian solution," Games and Economic Behavior, Elsevier, vol. 106(C), pages 179-187.
    19. Dietzenbacher, Bas & Dogan, Emre, 2024. "Population monotonicity and egalitarianism," Research Memorandum 007, Maastricht University, Graduate School of Business and Economics (GSBE).
    20. Sudhölter, Peter & Zarzuelo, José M., 2017. "Characterizations of highway toll pricing methods," European Journal of Operational Research, Elsevier, vol. 260(1), pages 161-170.

    More about this item

    Keywords

    cooperative game with transferable utilities; solution; self-covariance; consistent extensions; constrained egalitarianism.;
    All these keywords.

    JEL classification:

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

    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:hig:wpaper:85/ec/2014. 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: Shamil Abdulaev or Shamil Abdulaev (email available below). General contact details of provider: https://edirc.repec.org/data/hsecoru.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.