Membership separability: A new axiomatization of the Shapley value

The paper shows that Shapley's axiomatic characterization of his value can be strengthened considerably. Indeed, his additivity axiom can be replaced by a simple accounting property whereby a player's payoff is the difference of a reward based on the worth of coalitions to which she belongs, and a tax based on the worth of coalition to which she does not belong, without placing any restriction whatsoever on the functional relationship between the reward or the tax and the worths that determine them.