Cost allocation rule of minimum spanning tree problems without a supplier

Abstract

In this paper, the cost allocation problem of minimum spanning tree without a supplier has been discussed. By assigning nodes to play the role of supplier in turn, we can get n classic m.c.s.t.s. A cooperative cost game model is established whose cost function is defined on cost functions of the n classic m.c.s.t.s. We show that the cooperative game is totally balanced and it has a large core that includes each irreducible core of the classic m.c.s.t. mentioned above. As for a specific core allocation, the arithmetic mean of all Bird imputations is recommended.