IDEAS home Printed from https://ideas.repec.org/p/zbw/leiwps/113.html
   My bibliography  Save this paper

Null players, solidarity, and the egalitarian Shapley values

Author

Listed:
  • Casajus, André
  • Hüttner, Frank

Abstract

The Shapley value certainly is the most eminent single-point solution concept for TU-games. In its standard characterization, the null player property indicates the absence of solidarity among the players. First, we replace the null player property by a new axiom that guarantees null players non-negative payoffs whenever the grand coalition's worth is non-negative. Second, the equal treatment property is strengthened into desirability. This way, we obtain a new characterization of the class of egalitarian Shapley values, i.e., of convex combinations of the Shapley value and the equal division solution. We complement this result by characterizations of the class of generalized consensus values, i.e., of convex combinations of the Shapley value and the equal surplus division solution.

Suggested Citation

  • Casajus, André & Hüttner, Frank, 2012. "Null players, solidarity, and the egalitarian Shapley values," Working Papers 113, University of Leipzig, Faculty of Economics and Management Science.
  • Handle: RePEc:zbw:leiwps:113
    as

    Download full text from publisher

    File URL: https://www.econstor.eu/bitstream/10419/62126/1/722035187.pdf
    Download Restriction: no

    Other versions of this item:

    References listed on IDEAS

    as
    1. Grossmann, Volker & Steger, Thomas M. & Trimborn, Timo, 2013. "The macroeconomics of TANSTAAFL," Journal of Macroeconomics, Elsevier, vol. 38(PA), pages 76-85.
    2. Célestin Chameni Nembua & Nicolas Gabriel Andjiga, 2008. "Linear, efficient and symmetric values for TU-games," Economics Bulletin, AccessEcon, vol. 3(71), pages 1-10.
    3. Schäfer, Andreas & Schneider, Maik T., 2015. "Endogenous Enforcement Of Intellectual Property, North–South Trade, And Growth," Macroeconomic Dynamics, Cambridge University Press, vol. 19(05), pages 1074-1115, July.
    4. André Casajus, 2011. "Differential marginality, van den Brink fairness, and the Shapley value," Theory and Decision, Springer, vol. 71(2), pages 163-174, August.
    5. van den Brink, Rene, 2007. "Null or nullifying players: The difference between the Shapley value and equal division solutions," Journal of Economic Theory, Elsevier, vol. 136(1), pages 767-775, September.
    6. repec:ebl:ecbull:v:3:y:2008:i:71:p:1-10 is not listed on IDEAS
    7. Bretschger, Lucas & Steger, Thomas, 2013. "Globalization, The Volatility Of Intermediate Goods Prices, And Economic Growth," Macroeconomic Dynamics, Cambridge University Press, vol. 17(02), pages 402-430, March.
    8. McKinnon, Ronald & Schnabl, Gunther, 2008. "China's exchange rate impasse and the weak U.S. dollar," Working Papers 73, University of Leipzig, Faculty of Economics and Management Science.
    9. Chameni Nembua, C., 2012. "Linear efficient and symmetric values for TU-games: Sharing the joint gain of cooperation," Games and Economic Behavior, Elsevier, vol. 74(1), pages 431-433.
    10. Macho-Stadler, Ines & Perez-Castrillo, David & Wettstein, David, 2007. "Sharing the surplus: An extension of the Shapley value for environments with externalities," Journal of Economic Theory, Elsevier, vol. 135(1), pages 339-356, July.
    11. Nowak, Andrzej S & Radzik, Tadeusz, 1994. "A Solidarity Value for n-Person Transferable Utility Games," International Journal of Game Theory, Springer;Game Theory Society, vol. 23(1), pages 43-48.
    12. Ruiz, Luis M. & Valenciano, Federico & Zarzuelo, Jose M., 1998. "The Family of Least Square Values for Transferable Utility Games," Games and Economic Behavior, Elsevier, vol. 24(1-2), pages 109-130, July.
    13. repec:ebl:ecbull:v:3:y:2008:i:1:p:1-9 is not listed on IDEAS
    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. Casajus, André & Huettner, Frank, 2014. "On a class of solidarity values," European Journal of Operational Research, Elsevier, vol. 236(2), pages 583-591.
    2. Sylvain Béal & Eric Rémila & Philippe Solal, 2015. "A Class of Solidarity Allocation Rules for TU-games," Working Papers 2015-03, CRESE.
    3. Casajus, André & Yokote, Koji, 2017. "Weak differential marginality and the Shapley value," Journal of Economic Theory, Elsevier, vol. 167(C), pages 274-284.
    4. repec:spr:mathme:v:86:y:2017:i:1:d:10.1007_s00186-017-0587-z is not listed on IDEAS
    5. Tadeusz Radzik & Theo Driessen, 2016. "Modeling values for TU-games using generalized versions of consistency, standardness and the null player property," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 83(2), pages 179-205, April.
    6. Sylvain Béal & Eric Rémila & Philippe Solal, 2017. "Axiomatization and implementation of a class of solidarity values for TU-games," Theory and Decision, Springer, vol. 83(1), pages 61-94, June.
    7. Sylvain Béal & André Casajus & Frank Huettner & Eric Rémila & Philippe Solal, 2016. "Characterizations of weighted and equal division values," Theory and Decision, Springer, vol. 80(4), pages 649-667, April.
    8. Sylvain Ferrières, 2016. "Nullified equal loss property and equal division values," Working Papers 2016-06, CRESE.
    9. Casajus, André & Huettner, Frank, 2014. "Weakly monotonic solutions for cooperative games," Journal of Economic Theory, Elsevier, vol. 154(C), pages 162-172.
    10. Béal, Sylvain & Rémila, Eric & Solal, Philippe, 2015. "Preserving or removing special players: What keeps your payoff unchanged in TU-games?," Mathematical Social Sciences, Elsevier, vol. 73(C), pages 23-31.
    11. Sylvain Béal & Eric Rémila & Phillippe Solal, 2017. "Coalitional desirability and the equal division value," Working Papers 2017-08, CRESE.
    12. repec:kap:theord:v:83:y:2017:i:3:d:10.1007_s11238-017-9604-1 is not listed on IDEAS
    13. repec:spr:sochwe:v:49:y:2017:i:1:d:10.1007_s00355-017-1056-6 is not listed on IDEAS

    More about this item

    Keywords

    Solidarity; egalitarian Shapley value; equal division value; desirability; generalized consensus value;

    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
    • D60 - Microeconomics - - Welfare Economics - - - General

    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:zbw:leiwps:113. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (ZBW - German National Library of Economics). General contact details of provider: http://edirc.repec.org/data/vileide.html .

    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 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.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.