Allocation of fixed costsand the weighted Shapley value

The weighted value was introduced by Shapley in 1953 as an asymmetric version of his value. Since thenseveral axiomatizations have been proposed including one by Shapley in 1981 specifically addressed tocost allocation, a context in which weights appear naturally. It was at the occasion of a comment in whichhe only stated the axioms. The present paper offers a proof of Shapley's statement as well as analternative set of axioms. It is shown that the value is the unique rule which allocates additional fixedcosts fairly: only the players who are concerned contribute to the fixed cost and they contribute inproportion to their weights.....