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.operational research;cost allocation;game theory

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.

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

The P-Value for Cost Sharing in Minimum Cost Spanning Tree Situations

The aim of this paper is to introduce and axiomatically characterize the P-value as a rule to solve the cost sharing problem in minimum cost spanning tree (mcst) situations.The P-value is related to the Kruskal algorithm for finding an mcst.Moreover, the P-value leads to a core allocation of the corresponding mcst game, and when applied also to the mcst subsituations it delivers a population monotonic allocation scheme.A conewise positive linearity property is one of the basic ingredients of an axiomatic characterization of the P-value.costs;games;allocation;population

Connection Problems in Mountains and Monotonic Allocation Schemes

Directed minimum cost spanning tree problems of a special kind are studied,namely those which show up in considering the problem of connecting units (houses)in mountains with a purifier.For such problems an easy method is described to obtain a minimum cost spanning tree.The related cost sharing problem is tackled by considering thecorresponding cooperative cost game with the units as players and also the related connection games,for each unit one.The cores of the connection games have a simple structure and each core element can be extended to a population monotonic allocation scheme (pmas)and also to a bi-monotonic allocation scheme.These pmas-es for the connection games result in pmas-es for the cost game.cost allocation;operational research

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

No advantageous merging in minimum cost spanning tree problems

In the context of cost sharing in minimum cost spanning tree problems, we introduce a property called No Advantageous Merging. This property implies that no group of agents can be better off claiming to be a single node. We show that the sharing rule that assigns to each agent his own connection cost (the Bird rule) satisfies this property. Moreover, we provide a characterization of the Bird rule using No Advantageous Merging.Minimum cost spanning tree problems; cost sharing; Bird rule; No Advantageous Merging

Cost Monotonic "Cost and Charge" Rules for Connection Situations

The special class of conservative charge systems for minimum cost spanning tree (mcst) situations is introduced.These conservative charge systems lead to single-valued rules for mcst situations, which can also be described with the aid of obligation functions and are, consequently, cost monotonic.A value-theoretic interpretation of these rules is also provided.cost allocation;minimum cost spanning tree situations;cost monotonicity;sharing values

Additivity in cost spanning tree problems

We characterize a rule in 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. In both characterizations we can replace separability by population monotonicity.cost spanning tree problems additivity characterization