The balanced contributions property for symmetric players

This paper introduces a new relational axiom, the balanced contributions property for symmetric players, in TU cooperative games. It describes the fair treatment of symmetric players by restricting the requirement of the balanced contributions property to two symmetric players. Even under efficiency, our new axiom is logically independent of symmetry, which requires that symmetric players receive the same payoff. Nonetheless, in previous axiomatizations of an anonymous solution, replacing symmetry with our new axiom results in new axiomatizations of the solution.