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

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  • 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
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    File URL: http://www.beta-umr7522.fr/productions/publications/2011/2011-03.pdf
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    References listed on IDEAS

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    1. 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.
    2. 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.
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    Cited by:

    1. 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.
    2. 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.
    3. 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.
    4. DEHEZ, Pierre & FEREY, Samuel, 2012. "How to share joint liability: a cooperative game approach," CORE Discussion Papers 2012023, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    5. repec:wsi:igtrxx:v:19:y:2017:i:03:n:s0219198917500128 is not listed on IDEAS
    6. 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.

    More about this item

    Keywords

    cost allocation; Shapley value; fixed cost.;

    JEL classification:

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

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