IDEAS home Printed from https://ideas.repec.org/p/jrp/jrpwrp/2007-073.html
   My bibliography  Save this paper

The balanced solution for cooperative transferable utility games

Author

Listed:
  • Rene van den Brink

    (Department of Econometrics and Tinbergen Institute, Faculty of Economics and Business Administration, Free University Amsterdam)

  • Rene Levinsky

    (Max Planck Institute of Economics)

  • Miroslav Zeleny

    (Department of Mathematical Analysis, Faculty of Mathematics and Physics, Charles University, Czech Republic)

Abstract

The Shapley value of a cooperative transferable utility game distributes the dividend of each coalition in the game equally among its members. Given exogenous weights for all players, the corresponding weighted Shapley value distributes the dividends proportionally to their weights. In this contribution we deï¬ ne the balanced solution which assigns weights to players such that the corresponding weighted Shapley value of each player is equal to her weight. We prove its existence for all monotone transferable utility games, discuss other properties of this solution, and deal with its characterization through a reduced game consistency.

Suggested Citation

  • Rene van den Brink & Rene Levinsky & Miroslav Zeleny, 2007. "The balanced solution for cooperative transferable utility games," Jena Economics Research Papers 2007-073, Friedrich-Schiller-University Jena.
    • Handle: RePEc:jrp:jrpwrp:2007-073
    as

    Download full text from publisher

    File URL: https://oweb.b67.uni-jena.de/Papers/jerp2007/wp_2007_073.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. K. Michael Ortmann, 2000. "The proportional value for positive cooperative games," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 51(2), pages 235-248, April.
    2. Kalai, Ehud, 1977. "Proportional Solutions to Bargaining Situations: Interpersonal Utility Comparisons," Econometrica, Econometric Society, vol. 45(7), pages 1623-1630, October.
    3. Roth, Alvin E, 1979. "Proportional Solutions to the Bargaining Problem," Econometrica, Econometric Society, vol. 47(3), pages 775-777, May.
    4. Sergiu Hart, 2006. "Shapley Value," Discussion Paper Series dp421, The Federmann Center for the Study of Rationality, the Hebrew University, Jerusalem.
    5. Barry Feldman, 2000. "The Proportional Value of a Cooperative Game," Econometric Society World Congress 2000 Contributed Papers 1140, Econometric Society.
    Full references (including those not matched with items on IDEAS)

    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. René Brink & René Levínský & Miroslav Zelený, 2015. "On proper Shapley values for monotone TU-games," International Journal of Game Theory, Springer;Game Theory Society, vol. 44(2), pages 449-471, May.
    2. Rene (J.R.) van den Brink & Rene Levinsky & Miroslav Zeleny, 2018. "The Shapley Value, Proper Shapley Value, and Sharing Rules for Cooperative Ventures," Tinbergen Institute Discussion Papers 18-089/II, Tinbergen Institute.
    3. Radzvilas, Mantas, 2016. "Hypothetical Bargaining and the Equilibrium Selection Problem in Non-Cooperative Games," MPRA Paper 70248, University Library of Munich, Germany.
    4. Nejat Anbarci & Ching-jen Sun, 2011. "Distributive justice and the Nash bargaining solution," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 37(3), pages 453-470, September.
    5. Ismail Saglam, 2013. "Endogenously proportional bargaining solutions," Economics Bulletin, AccessEcon, vol. 33(2), pages 1521-1534.
    6. Bas Dietzenbacher & Hans Peters, 2022. "Characterizing NTU-bankruptcy rules using bargaining axioms," Annals of Operations Research, Springer, vol. 318(2), pages 871-888, November.
    7. Manfred Besner, 2020. "Value dividends, the Harsanyi set and extensions, and the proportional Harsanyi solution," International Journal of Game Theory, Springer;Game Theory Society, vol. 49(3), pages 851-873, September.
    8. Elvio Accinelli-Gamba & Leobardo Plata-Pérez & Joss Sánchez-Pérez, 2014. "Efficiency, egalitarianism, stability and social welfare in infinite dimensional economies," Ensayos Revista de Economia, Universidad Autonoma de Nuevo Leon, Facultad de Economia, vol. 0(1), pages 1-26, May.
    9. Ismail Saglam, 2014. "A Simple Axiomatization Of The Egalitarian Solution," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 16(04), pages 1-7.
    10. Barry Feldman, 2005. "Lost in Translation? Basis Utility and Proportionality in Games," Game Theory and Information 0507001, University Library of Munich, Germany, revised 28 Feb 2006.
    11. Laurens Cherchye & Thomas Demuynck & Bram De Rock, 2013. "Nash‐Bargained Consumption Decisions: A Revealed Preference Analysis," Economic Journal, Royal Economic Society, vol. 123, pages 195-235, March.
    12. Adib Bagh & Josh Ederington, 2024. "Equity‐efficiency tradeoffs in international bargaining," Economic Inquiry, Western Economic Association International, vol. 62(2), pages 782-804, April.
    13. Barry Feldman, 2002. "A Dual Model of Cooperative Value," Game Theory and Information 0207001, University Library of Munich, Germany.
    14. Driesen, Bram, 2016. "Truncated Leximin solutions," Mathematical Social Sciences, Elsevier, vol. 83(C), pages 79-87.
    15. Navarro, Noemí & Veszteg, Róbert F., 2020. "On the empirical validity of axioms in unstructured bargaining," Games and Economic Behavior, Elsevier, vol. 121(C), pages 117-145.
    16. Sergei Pechersky, 2001. "On Proportional Excess for NTU Games," EUSP Department of Economics Working Paper Series 2001/02, European University at St. Petersburg, Department of Economics, revised 30 Oct 2001.
    17. Marco Mariotii, 1996. "Fair bargains: distributive justice and Nash Bargaining Theory," Game Theory and Information 9611003, University Library of Munich, Germany, revised 06 Dec 1996.
    18. Manfred Besner, 2019. "Axiomatizations of the proportional Shapley value," Theory and Decision, Springer, vol. 86(2), pages 161-183, March.
    19. Besner, Manfred, 2018. "Weighted Shapley hierarchy levels values," MPRA Paper 88160, University Library of Munich, Germany.
    20. Besner, Manfred, 2017. "Axiomatizations of the proportional Shapley value," MPRA Paper 82990, University Library of Munich, Germany.

    More about this item

    Keywords

    Balanced solution; Proportionality; Reduced game consistency; Weighted Shapley value.;
    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:jrp:jrpwrp:2007-073. 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: Markus Pasche (email available below). General contact details of provider: http://www.jenecon.de .

    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.