A cooperative game with transferable utilities, or simply aTU-game, describes a situation in which players can obtain certainpayoffs by cooperation. A solution mapping for these games is amapping which assigns to every game a set of payoff distributionsover the players in the game. Well-known solution mappings are the Coreand the Weber set. In this paper we consider the mapping assigning toevery game the Harsanyi set being the set of payoff vectors obtained byall possible distributions of the Harsanyi dividends of a coalitionamongst its members. We discuss the structure and properties of thismapping and show how the Harsanyi set is related to the Core and Weberset. We also characterize the Harsanyi mapping as the unique mappingsatisfying a set of six axioms. Finally we discuss some properties of theHarsanyi Imputation set, being the individally rational subset of theHarsanyi set.