On the Aumann–Shapley value

Abstract

Let L be a D-lattice, i.e. a lattice ordered effect algebra, and let BV be the Banach space of all real-valued functions of bounded variation on L (vanishing at 0) endowed with the variation norm. We prove the existence of a continuous Aumann–Shapley value φ on NA, the subspace of BV spanned by all functions of the form f°µ, where µ:L->[0,1] is a non-atomic σ-additive modular measure and f:[0,1]->R is of bounded variation and continuous at 0 and at