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Allocation of fixed costs and the weighted Shapley value

Author

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  • DEHEZ, Pierre

    () (Université catholique de Louvain (UCL). Center for Operations Research and Econometrics (CORE))

Abstract

The weighted value was introduced by Shapley in 1953 as an asymmetric version of his value. Since then several approximations 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

  • DEHEZ, Pierre, 2009. "Allocation of fixed costs and the weighted Shapley value," CORE Discussion Papers 2009035, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  • Handle: RePEc:cor:louvco:2009035
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    File URL: http://www.uclouvain.be/cps/ucl/doc/core/documents/dp2009_35web.pdf
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    Cited by:

    1. Pierre Dehez, 2010. "Cooperative provision of indivisible public goods," Working Papers of BETA 2010-14, Bureau d'Economie Théorique et Appliquée, UDS, Strasbourg.

    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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