Minimum cost spanning tree games and population monotonic allocation schemes

In this paper we present the Subtraction Algorithm that computes for every classical minimum cost spanning tree game a population monotonic allocation scheme. As a basis for this algorithm serves a decomposition theorem that shows that every minimum cost spanning tree game can be written as nonnegative combination of minimum cost spanning tree games corresponding to 0–1 cost functions. It turns out that the Subtraction Algorithm is closely related to the famous algorithm of Kruskal for the determination of minimum cost spanning trees. For variants of the classical minimum cost spanning tree games we show that population monotonic allocation schemes do not necessarily exist.