Decomposable Effectivity Functions

Decomposable effectivity functions are introduced as an extension of additive effectivity functions. Whereas additive effectivity functions are determined by pairs of additive TU-games, decomposable effectivity functions are generated by pairs of TU-games that need not be additive. It turns out that the class of decomposable effectivity functions does not only contain the class of additive effectivity functions but it also contains the class of effectivity functions corresponding to simple games and the class of effectivity functions corresponding to veto functions. We examine relations between properties of decomposable effectivity functions and the TU-games by which they are generated. It turns out that a decomposable effectivity function is stable whenever it can be generated by a pair of balanced TU-utility games. Finally, we provide two characterizations of decomposable effectivity functions.