A new weight scheme for the Shapley value

It is well known since Owen (Owen, G., 1968. A note on the Shapley value. Management Science 14, 731–732.) that the weights in the weighted Shapley value cannot be interpreted as a measure of power (i.e., of the ability to bargain) of the players. We propose in this paper a new weight scheme for the Shapley value, which allows to interpret weights as bargaining power measure. We provide an axiomatic characterization of this new weighted Shapley value.