We derive an explicit formula for a marginalist and efficient value for TU game which possesses the null-player property and is either continuous or monotonic. We show that every such value has to be additive and covariant as well. It follows that the set of all marginalist, efficient, and monotonic values possessing the null-player property coincides with the set of random-order values, and, thereby, the last statement provides an axiomatization without the linearity axiom for the latter which is similar to that of Young for the Shapley value. Another axiomatization without linearity for random-order values is provided by marginalism, efficiency, monotonicity and covariance.
- Axiomatic characterization
- Transferable utility game