Consistency distinguishes the (weighted) Shapley value, the (weighted) surplus division value and the prenucleolus

Abstract

On the domain of cooperative games with transferable utility, we investigate how the main results in Hart and Mas-Colell (1989) vary when we replace self consistency by projected consistency or max consistency. As a consequence, we obtain several axiomatic comparison among the (weighted) Shapley value, the (weighted) surplus division solution and the prenucleolus.