This paper defines a multichoice \(n\)-player cooperative game in characteristic function form that permits to each player the \(m+1\) actions of working at any of \(m+1\) different levels, including the level of doing nothing. This last level is effectively ignored in generalizing the classical concept of value or power index from an \(n\)-dimensional row vector to an \(m\times n\) matrix of values or power index vectors for each (nondegenerate) action. Weights are defined for each action, and a set of four axioms is proved to imply the uniqueness of the generalized value for any given set of weights. An explicit formula for the generalized value is given and it is shown to reduce to the Shapley value in the case of a single nondegenerate action.