Additivity in minimum cost spanning tree problems

Abstract

We characterize a rule in minimum cost spanning tree problems using an additivity property and some basic properties. If the set of possible agents has at least three agents, these basic properties are symmetry and separability. If the set of possible agents has two agents, we must add positivity.JEL Codes: C71, D70, D85.

A characterization of Kruskal sharing rules for minimum cost spanning tree problems

“…This characterization is based on a property of monotonicity over the set of agents and a property of additivity defined in Bergantiños and Vidal-Puga (2004). This result holds for any set of possible agents N except for two-agent sets.…”

“…For this reason Bergantiños and Vidal-Puga (2004) introduce the constrained additivity property. In order to define this property we need to introduce the concept of similar problems.…”

“…Following similar arguments to Bergantiños and Vidal-Puga (2004), we consider T 1 r = {i ∈ T r : c 0i = x} ∪ {j} and T 2 r = {i ∈ T r : c 0i = 0} \ {j}.…”

“…Kar (2002) studied the Shapley value of this game whereas Huberman (1981 and1984) studied the core and the nucleolus. Feltkamp et al (1994) introduced the equal remaining obligation rule, which was studied by Bergantiños and Vidal-Puga (2004, 2007a, and 2007b. This rule belongs to a wide family of rules, introduced by Tijs et al (2006), the family of obligation rules.…”

The folk solution and Boruvka’s algorithm in minimum cost spanning tree problems

“…The rules introduced by Bergantiños and Vidal-Puga [2], Feltkamp et al [12] coincide [1]. We call this rule the folk solution, which can be obtained in other ways (see [7,8,[2][3][4]). …”