Directed minimum cost spanning tree problems of a special kind are studied, namely those which show up in considering the problem of connecting units (houses) in mountains with a purifier. For such problems an easy method is described to obtain a minimum cost spanning tree. The related cost sharing problem is tackled by considering the corresponding cooperative cost game with the units as players and also the related connection games, for each unit one. The cores of the connection games have a simple structure and each core element can be extended to a population monotonic allocation scheme (pmas) and also to a bi-monotonie allocation scheme. These pmas-es for the connection games result in pmas-es for the cost game.

Different axiomatic systems for the Shapley value can be found in the literature. For games with a coalition structure, the Shapley value also has been axiomatized in several ways. In this paper, we discuss a generalization of the Shapley value to the class of partition function form games. The concepts and axioms, related to the Shapley value, have been extended and a characterization for the Shapley value has been provided. Finally, an application of the Shapley value is given.