Marginalism and the Shapley value

We survey axiomatic results concerning the Shapley value (Shapley (1953)). This marginalist allocation rule results from an axiomatic study of the class of coalitional games. Shapley (1953) specifies a list of desirable properties of solutions for this class of games, and he shows that the combination of these properties determines a unique allocation rule, now called the Shapley value. Several authors have enriched Shapley’s axiomatic study and have provided new characterizations of this allocation rule. The aim of this article is to put into perspective these characterizations. We highlight the logical relations between the axioms. Moreover, we show how the marginalist criterion, which was not explicitely present in Shapley’s characterisation, is progressively introduced into the axiomatic.