Allocation of fixed costs: characterization of the (dual) weighted Shapley value
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.
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- Thierry Burger-Helmchen & Laurence Frank, 2011.
"La création de rentes : une approche par les compétences et capacités dynamiques,"
Working Papers of BETA
2011-01, Bureau d'Economie Théorique et Appliquée, UDS, Strasbourg.
- 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.
- Pierre Dehez, 2011. "Allocation Of Fixed Costs: Characterization Of The (Dual) Weighted Shapley Value," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 13(02), pages 141-157.
- René van den Brink, 2002. "An axiomatization of the Shapley value using a fairness property," International Journal of Game Theory, Springer, vol. 30(3), pages 309-319.
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