The Public Good index for games with several levels of approval in the input and output

The Public Good index is a power index for simple games introduced by Holler and later axiomatized by Holler and Packel, so that some authors also speak of the Holler--Packel index. A generalization to the class of games with transferable utility was given by Holler and Li. Here we generalize the underlying ideas to games with several levels of approval in the input and output -- so-called $(j,k)$ simple games. Corresponding axiomatizations are also provided.