IDEAS home Printed from https://ideas.repec.org/p/ulp/sbbeta/2011-03.html
   My bibliography  Save this paper

Allocation of fixed costs: characterization of the (dual) weighted Shapley value

Author

Listed:
  • Pierre Dehez

Abstract

The weighted value was introduced by Shapley in 1953 as an asymmetric version of his value. Since then several axiomatizations have been proposed including one by Shapley in 1981 specifically addressed to cost allocation, a context in which weights appear naturally. It was at the occasion of a comment in which he only stated the axioms. The present paper offers a proof of Shapley's statement as well as an alternative set of axioms. It is shown that the value is the unique rule that allocates additional fixed costs fairly: only the players who are concerned contribute to the fixed cost and they contribute in proportion to their weights. A particular attention is given to the case where some players are assigned a zero weight.

Suggested Citation

  • Pierre Dehez, 2011. "Allocation of fixed costs: characterization of the (dual) weighted Shapley value," Working Papers of BETA 2011-03, Bureau d'Economie Théorique et Appliquée, UDS, Strasbourg.
    • Handle: RePEc:ulp:sbbeta:2011-03
    as

    Download full text from publisher

    File URL: http://beta.u-strasbg.fr/WP/2011/2011-03.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. René van den Brink, 2002. "An axiomatization of the Shapley value using a fairness property," International Journal of Game Theory, Springer;Game Theory Society, vol. 30(3), pages 309-319.
    2. Pierre Dehez & Daniela Tellone, 2013. "Data Games: Sharing Public Goods with Exclusion," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 15(4), pages 654-673, August.
    3. William Thomson, 2007. "Cost allocation and airport problems," RCER Working Papers 537, University of Rochester - Center for Economic Research (RCER).
    4. Thierry Burger-Helmchen & Laurence Frank, 2011. "La création de rentes : une approche par les compétences et capacités dynamiques," Innovations, De Boeck Université, vol. 0(2), pages 89-111.
    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. Julien Jacob, 2011. "Innovation and diffusion in risky industries under liability law: the case of “double-impact” innovations," Working Papers of BETA 2011-24, Bureau d'Economie Théorique et Appliquée, UDS, Strasbourg.
    2. Jenny Monheim-Helstroffer & Marie Obidzinski, 2011. "The EU legislation game: the case of asylum law," Working Papers of BETA 2011-16, Bureau d'Economie Théorique et Appliquée, UDS, Strasbourg.
    3. Demuynck, Thomas & Rock, Bram De & Ginsburgh, Victor, 2016. "The transfer paradox in welfare space," Journal of Mathematical Economics, Elsevier, vol. 62(C), pages 1-4.
    4. Pierre Dehez, 2017. "On Harsanyi Dividends and Asymmetric Values," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 19(03), pages 1-36, September.
    5. Samuel Ferey & Pierre Dehez, 2016. "Multiple Causation, Apportionment, and the Shapley Value," The Journal of Legal Studies, University of Chicago Press, vol. 45(1), pages 143-171.
    6. Dehez, Pierre & Ferey, Samuel, 2013. "How to share joint liability: A cooperative game approach," Mathematical Social Sciences, Elsevier, vol. 66(1), pages 44-50.
    7. Pierre Dehez & Daniela Tellone, 2013. "Data Games: Sharing Public Goods with Exclusion," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 15(4), pages 654-673, August.
    8. Pierre Dehez, 2013. "Cooperative provision of indivisible public goods," Theory and Decision, Springer, vol. 74(1), pages 13-29, January.
    9. Radzik, Tadeusz, 2012. "A new look at the role of players’ weights in the weighted Shapley value," European Journal of Operational Research, Elsevier, vol. 223(2), pages 407-416.
    10. Meixing Dai, 2011. "Motivations and strategies for a real revaluation of the Yuan," Working Papers of BETA 2011-23, Bureau d'Economie Théorique et Appliquée, UDS, Strasbourg.
    11. Houda Ghaya, 2011. "Board of Directors’ Involvement in Strategic Decision Making Process: Definition and Literature Review," Working Papers of BETA 2011-22, Bureau d'Economie Théorique et Appliquée, UDS, Strasbourg.
    12. Besner, Manfred, 2018. "Player splitting, players merging, the Shapley set value and the Harsanyi set value," MPRA Paper 87125, University Library of Munich, Germany.

    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. Pierre Dehez, 2013. "Cooperative provision of indivisible public goods," Theory and Decision, Springer, vol. 74(1), pages 13-29, January.
    2. Pierre Dehez & Daniela Tellone, 2013. "Data Games: Sharing Public Goods with Exclusion," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 15(4), pages 654-673, August.
    3. Cubukcu, K. Mert, 2020. "The problem of fair division of surplus development rights in redevelopment of urban areas: Can the Shapley value help?," Land Use Policy, Elsevier, vol. 91(C).
    4. Meixing Dai, 2011. "Motivations and strategies for a real revaluation of the Yuan," Working Papers of BETA 2011-23, Bureau d'Economie Théorique et Appliquée, UDS, Strasbourg.
    5. Julien Jacob, 2011. "Innovation and diffusion in risky industries under liability law: the case of “double-impact” innovations," Working Papers of BETA 2011-24, Bureau d'Economie Théorique et Appliquée, UDS, Strasbourg.
    6. Jenny Monheim-Helstroffer & Marie Obidzinski, 2011. "The EU legislation game: the case of asylum law," Working Papers of BETA 2011-16, Bureau d'Economie Théorique et Appliquée, UDS, Strasbourg.
    7. Márkus, Judit & Pintér, Miklós & Radványi, Anna, 2011. "The Shapley value for airport and irrigation games," MPRA Paper 30031, University Library of Munich, Germany.
    8. Sylvain Béal & Marc Deschamps & Philippe Solal, 2014. "Balanced collective contributions, the equal allocation of non-separable costs and application to data sharing games," Working Papers hal-01377926, HAL.
    9. Sylvain Béal & Mostapha Diss & Rodrigue Tido Takeng, 2024. "New axiomatizations of the Diversity Owen and Shapley values," Working Papers 2024-09, CRESE.
    10. René Brink & Yukihiko Funaki, 2009. "Axiomatizations of a Class of Equal Surplus Sharing Solutions for TU-Games," Theory and Decision, Springer, vol. 67(3), pages 303-340, September.
    11. Streekstra, Leanne & Trudeau, Christian, 2020. "Stable source connection and assignment problems as multi-period shortest path problems," Discussion Papers on Economics 7/2020, University of Southern Denmark, Department of Economics.
    12. René Brink & Frank Steffen, 2012. "Axiomatizations of a positional power score and measure for hierarchies," Public Choice, Springer, vol. 151(3), pages 757-787, June.
    13. Hougaard, Jens Leth & Moulin, Hervé, 2014. "Sharing the cost of redundant items," Games and Economic Behavior, Elsevier, vol. 87(C), pages 339-352.
    14. René Brink & Youngsub Chun, 2012. "Balanced consistency and balanced cost reduction for sequencing problems," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 38(3), pages 519-529, March.
    15. Algaba, Encarnación & Béal, Sylvain & Fragnelli, Vito & Llorca, Natividad & Sánchez-Soriano, Joaquin, 2019. "Relationship between labeled network games and other cooperative games arising from attributes situations," Economics Letters, Elsevier, vol. 185(C).
    16. Harald Wiese, 2012. "Values with exogenous payments," Theory and Decision, Springer, vol. 72(4), pages 485-508, April.
    17. Dehez, Pierre & Ferey, Samuel, 2013. "How to share joint liability: A cooperative game approach," Mathematical Social Sciences, Elsevier, vol. 66(1), pages 44-50.
    18. van den Brink, René & Núñez, Marina & Robles, Francisco, 2021. "Valuation monotonicity, fairness and stability in assignment problems," Journal of Economic Theory, Elsevier, vol. 195(C).
    19. Zou, Zhengxing & van den Brink, René, 2020. "Equal loss under separatorization and egalitarian values," Economics Letters, Elsevier, vol. 194(C).
    20. Paula Jaramillo, 2013. "Congestion in irrigation problems," Documentos CEDE 10553, Universidad de los Andes, Facultad de Economía, CEDE.

    More about this item

    Keywords

    cost allocation; Shapley value; fixed cost.;
    All these keywords.

    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
    • D46 - Microeconomics - - Market Structure, Pricing, and Design - - - Value Theory

    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:ulp:sbbeta:2011-03. 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: the person in charge (email available below). General contact details of provider: https://edirc.repec.org/data/bestrfr.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.