Minimum cost spanning tree games and population monotonic allocation schemes

Abstract

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.

A monotonic and merge-proof rule in minimum cost spanning tree situations

“…A stronger version of core selection is population monotonicity, which requires that the cost allocated to any agent will not decrease if new agents join the society. Population monotonicity in mcst problems has been studied by Bergantiños and Gómez-Rúa (2010), Vidal-Puga (2007a, 2009), Bogomolnaia and Moulin (2010), Lorenzo-Freire (2009), andNorde et al (2004).…”

Computation of the Shapley value of minimum cost spanning tree games: #P-hardness and polynomial cases

“…Furthermore, we have the following proposition due to Norde, Moretti and Tijs [19]. The proof is essentially the same as that of [19] but is slightly shorter.…”

“…See, e.g., [8], [19], [17], [11] and [7]. In contrast, there is only few literature on the computational complexity of MCST games.…”

Minimum cost arborescences

“…6 This is a term coined by because this allocation rule has been independently proposed and analyzed in a number of papers. See, for instance, Bergantinos and Vidal-Puga (2007a), Bergantinos and Vidal-Puga (2007b), , Branzei et al (2004), Feltkamp et al (1994, Norde et al (2001) Branzei et al (2005).…”