Shapley's Non-transferable Utility Value correspondence is characterized by a set of axioms, which combine the features of the axioms for the value of transferable utility games, and those for Nash's solution to the bargaining problem. The axioms refer to values as payoff vectors only--the comparison weights associated with a value make no explicit appearance. A key axiom is conditional additivity, which may be stated as follows: If the same payoff vector is a value of each of two games, then it is also a value of the half-half probability combination of these two games, unless it is Pareto-dominated there. For the axioms to work, the boundary of the set of feasible outcomes must be smooth.