We extend the Aumann-Shapley value to mixed action-set games, i.e., multilevel TU games where there are simultaneously two types of players: discrete players that possess a finite number of activity levels in which they can join a coalition, and continuous players that possess a continuum of levels.

We consider the problem of how to distribute public expenditure among the different regions of an economic entity after all taxes have been collected. Typical examples are: the regions that make up a country, the states of a federal country, or the countries of a confederation of countries. We...