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.

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

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

The NTU consistent coalitional value

We introduce a new value for NTU games with coalition structure. This value coincides with the consistent value for trivial coalition structures, and with the Owen value for TU games with coalition structure. Furthermore, we present two characterizations: the first one using a consistency property and the second one using balanced contributions properties.consistent coalition structure value NTU balanced contributions

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

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

Defining rules in cost spanning tree problems through the canonical form

We define the canonical form of a cost spanning tree problem. The canonical form has the property that reducing the cost of any arc, the minimal cost of connecting agents to the source is also reduced. We argue that the canonical form is a relevant concept in this kind of problems and study a rule using it. This rule satisfies much more interesting properties than other rules in the literature. Furthermore we provide two characterizations. Finally, we present several approaches to this rule without using the canonical form.cost spanning tree problems canonical form rules

Defining Rules in Cost Spanning Tree Problems Through the Canonical Form

We define the canonical form of a cost spanning tree problem. The canonical form has the property that reducing the cost of any arc, the minimal cost of connecting agents to the source is also reduced. We argue that the canonical form is a relevant concept in this kind of problems and study a rule using it. This rule satisfies much more interesting properties than other rules in the literature. Furthermore we provide two characterizations. Finally, we present several approaches to this rule without using the canonical form.Cost spanning tree, Rules, Canonical form

One-way and two-way cost allocation in hub network problems

We study hub problems where a set of nodes send and receive data from each other. In order to reduce costs, the nodes use a network with a given set of hubs. We address the cost sharing aspect by assuming that nodes are only interested in either sending or receiving data, but not both (one-way flow) or that nodes are interested in both sending and receiving data (two-way flow). In both cases, we study the non-emptiness of the core and the Shapley value of the corresponding cost game