Marginalist and Efficient Values for TU Games

Anna B. Khmelnitskaya

We derive an explicit formula for a marginalist and efficient value for a TU game which possesses the -player property and is either continuous or monotonic. We show that every such a value has to be additive and covariant as well. It follows that the set of all marginalist, efficient, and monotonic values possessing the -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. Keywords: Transferable utility game; Value; Axiomatic characterization; Efficiency; Mar- ginalism

January, 1999
Published in: 
Mathematical Social Sciences 38 (1999), 45-54.