Cost monotonicity, consistency and minimum cost spanning tree games

We propose a new cost allocation rule for minimum cost spanning tree games. The new rule is a core selection and also satisfies cost monotonicity. We also give characterization theorems for the new rule as well as the much-studied Bird allocation. We show that the principal difference between these two rules is in terms of their consistency properties

Cost monotonicity, consistency and minimum cost spanning tree games

We propose a new cost allocation rule for minimum cost Spanning tree games. The new rule is a core selection and also satisfices cost monotonicity. We also give charqcterization theorems for the new rule as well as the much-studied Bird allocation. We show that the principal difference between these two rules is interms of their consistency properties.spanning tree, cost allocation, core selection, cost monotonicity, consistency

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

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

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

AbstractBoruvka’s algorithm, which computes a minimum cost spanning tree, is used to define a rule to share the cost among the nodes (agents). We show that this rule coincides with the folk solution, a very well-known rule of this literature

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

The Boruvka's algorithm, which computes the minimum cost spanning tree, is used to define a rule to share the cost among the nodes (agents). We show that this rule coincides with the folk solution, a very well-known rule of this literature.minimum cost spanning tree; Boruvka's algorithm; folk solution

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

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

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

Cost allocation protocols for network formation on connection situations

International audienceThe issue of embedding cost-awareness in the design of communication network devices and protocols has been growing at a fast rate in last years. Under certain connection situations, however, network design is not enforced by a central authority. This is the case, for instance, of power control for wireless networks, where the cost of a link is a function of the power needed to send a message to a remote node, which increases with the distance. Here each player wishes to consume as few power as possible to send its request and the main question is how to avoid that players deviate from a socially optimal network. In this paper, we study strategic games based on connection situations with the objective to coordinate self-interested agents placed on the nodes of a graph to realize a more efficient communication network. We address the problem of the design of cost allocation protocols that may guarantee the convergence of the best response dynamic and we analyze the effects of cost monotonicity and other state-dependent properties on the optimality of a protocol