The balanced contribution

We introduce a new axiom, the balanced contributions property for equal contributors. This axiom is defined by restricting the requirement of the balanced contributions property (Myerson (1980)) to two players whose contributions to the grand coalition are the same. We prove that this axiom, together with efficiency and weak covariance, characterizes a new class of solutions, the r-egalitarian Shapley values. This class subsumes many variants of the Shapley value, e.g., the egalitarian Shapley values or the discounted Shapley values. Our characterization uncovers a common property for many variants of the Shapley value, as well as provides a new method for characterizing them. Based on our new axiom, we also provide a non-cooperative implementation of the r-egalitarian Shapley values. Our new mechanism clarifies the difference among variants of the Shapley value from the bargaining power of players affected by the cost of continuing a bargaining.