Sign symmetry vs symmetry: Young's characterization of the Shapley value revisited

We revisit Young's (Young, 1985) characterization of the Shapley value by efficiency, symmetry, and marginality/strong monotonicity. In particular, we suggest a relaxation of symmetry called sign symmetry. While symmetry requires equally productive players to obtain the same payoffs, sign symmetry only requires their payoffs to have the same sign. It turns out that sign symmetry can take the place of symmetry in Young's characterization.