OBLIGATION RULES

We provide a characterization of the obligation rules in the context of minimum cost spanning tree games. We also explore the relation between obligation rules and random order values of the irreducible cost game - it is shown that the later is a subset of the obligation rules. Moreover we provide a necessary and sucient condition on obligation function such that the corresponding obligation rule coincides with a random order value.

A Vertex Oriented Approach to Minimum Cost Spanning Tree Problems

In this paper we consider spanning tree problems, where n players want to be connected to a source as cheap as possible. We introduce and analyze (n!) vertex oriented construct and charge procedures for such spanning tree situations leading in n steps to a minimum cost spanning tree and a cost sharing where each player pays the edge which he chooses in the procedure. The main result of the paper is that the average of the n! cost sharings provided by our procedure is equal to the P-value for minimum cost spanning tree situations introduced and characterized by Branzei et al. (2004). As a side product, we find a new method, the vertex oriented procedure, to construct minimum cost spanning trees.Minimum cost spanning tree games;algorithm;value;cost sharing

Minimum Cost Arborescences

In this paper, we analyze the cost allocation problem when a group of agents or nodes have to be connected to a source, and where the cost matrix describing the cost of connecting each pair of agents is not necessarily symmetric, thus extending the well-studied problem of minimum cost spanning tree games, where the costs are assumed to be symmetric. The focus is on rules which satisfy axioms representing incentive and fairness properties. We show that while some results are similar, there are also signifcant differences between the frameworks corresponding to symmetric and asymmetric cost matrices.directed networks ; cost allocation ; core stability ; continuity ; cost monotonicity

Minimum cost arborescences

In this paper, we analyze the cost allocation problem when a group of agents or nodes have to be connected to a source, and where the cost matrix describing the cost of connecting each pair of agents is not necessarily symmetric, thus extending the well-studied problem of minimum cost spanning tree games, where the costs are assumed to be symmetric. The focus is on rules which satisfy axioms representing incentive and fairness properties. We show that while some results are similar, there are also signilcant dikerences between the frameworks corresponding to symmetric and asymmetric cost matrices.directed networks, cost allocation, core stability, continuity, cost monotonicity

Realizing efficient outcomes in cost spanning problems

We propose a simple non-cooperative mechanism of network formation in cost spanning tree problems. The only subgame equilibrium payoff is efficient. Moreover, we extend the result to the case of budget restrictions. The equilibrium payoff can them be easily adapted to the framework of Steiner trees.efficiency, cost spanning tree problem, cost allocation, network formation, subgame perfect equilibrium, budget restrictions, Steiner trees

Cost additive rules in minimum cost spanning tree problems with multiple sources

In this paper, we introduce a family of rules in minimum cost spanning tree problems with multiple sources called Kruskal sharing rules. This family is characterized with cone wise additivity and independence of irrelevant trees . We also investigate some subsets of this family and provide their axiomatic characterizations. The first subset is obtained by adding core selection. The second one is obtained by adding core selection and equal treatment of source cost

The folk rule through a painting procedure for minimum cost spanning tree problems with multiple sources

We consider minimum cost spanning tree problems with multiple sources. We propose a cost allocation rule based on a painting procedure. Agents paint the edges on the paths connecting them to the sources. We prove that the painting rule coincides with the folk rule

Cooperative games for minimum cost spanning tree problems

Minimum cost spanning tree problems are well known problems in the Operations Research literature. Some agents, located at different geographical places, want a service provided by a common supplier. Agents will be served through costly connections. Some part of the literature has focused, mainly, in studying how to allocate the connection cost among the agents. We review the papers that have addressed the allocation problem using cooperative game theory