The irreducible Core of a minimum cost spanning tree game

It is a known result that for a minimum cost spanning tree (mcst) game a Core allocation can be deduced directly from a mcst in the underlying network. To determine this Core allocation one only needs to determine a mcst in the network and it is not necessary to calculate the coalition values of the corresponding mcst game. In this paper we will deduce other Core allocations directly from the network, without determining the corresponding mcst game itself: we use an idea of Bird (cf. [4]) to present two procedures that determine a part of the Core (called the Irreducible Core) from the network

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

On the Shapley value of a minimum cost spanning tree problem

We associate an optimistic coalitional game with each minimum cost spanning tree problem. We define the worth of a coalition as the cost of connection assuming that the rest of the agents are already connected. We define a cost sharing rule as the Shapley value of this optimistic game. We prove that this rule coincides with a rule present in the literature under different names. We also introduce a new characterization using a property of equal contributions.minimum cost spanning tree problems Shapley value

A fair rule in minimum cost spanning tree problems

We study minimum cost spanning tree problems and define a cost sharing rule that satisfies many more properties than other rules in the literature. Furthermore, we provide an axiomatic characterization based on monotonicity properties.minimum cost spanning tree, cost sharing

Bird's tree allocations revisited

Game Theory;Cost Allocation

The Bird Core for Minimum Cost Spanning Tree problems Revisited: Monotonicity and Additivity Aspects

A new way is presented to define for minimum cost spanning tree (mcst-) games the irreducible core, which is introduced by Bird in 1976.The Bird core correspondence turns out to have interesting monotonicity and additivity properties and each stable cost monotonic allocation rule for mcst-problems is a selection of the Bird core correspondence.Using the additivity property an axiomatic characterization of the Bird core correspondence is obtained.cost allocation;minimum cost spanning tree games;Bird core;cost monotonicity;cone additivity

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.

Decentralized Pricing in Minimum Cost Spanning Trees

In the minimum cost spanning tree model we consider decentralized pricing rules, i.e. rules that cover at least the efficient cost while the price charged to each user only depends upon his own connection costs. We define a canonical pricing rule and provide two axiomatic characterizations. First, the canonical pricing rule is the smallest among those that improve upon the Stand Alone bound, and are either superadditive or piece-wise linear in connection costs. Our second, direct characterization relies on two simple properties highlighting the special role of the source cost.pricing rules; minimum cost spanning trees; canonical pricing rule; stand-alone cost; decentralization