  Modal logics for reasoning about the power of coalitions capture the notion
of effectivity functions associated with game forms. The main goal of coalition
logics is to provide formal tools for modeling the dynamics of a game frame
whose states may correspond to different game forms. The two classes of
effectivity functions studied are the families of playable and truly playable
effectivity functions, respectively. In this paper we generalize the concept of
effectivity function beyond the yes/no truth scale. This enables us to describe
the situations in which the coalitions assess their effectivity in degrees,
based on functions over the outcomes taking values in a finite {\L}ukasiewicz
chain. Then we introduce two modal extensions of {\L}ukasiewicz finite-valued
logic together with many-valued neighborhood semantics in order to encode the
properties of many-valued effectivity functions associated with game forms. As
our main results we prove completeness theorems for the two newly introduced
modal logics.
