Henk Norde

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. (This abstract was borrowed from another version of this item.) (This abstract was borrowed from another version of this item.) (This abstract was borrowed from another version of this item.)

The Shapley Value for Partition Function Form Games

Different axiomatizations of the Shapley value for TU games can be found in the literature. The Shapley value has been generalized in several ways to the class of games in partition function form. In this paper we discuss another generalization of the Shapley value and provide a characterization.

Obligation Rules for Minimum Cost Spanning Tree Situations and Their Monotonicity Properties

We introduce the class of Obligation rules for minimum cost spanning tree situations.The main result of this paper is that such rules are cost monotonic and induce also population monotonic allocation schemes.Another characteristic of Obligation rules is that they assign to a minimum cost spanning tree situation a vector of cost contributions which can be obtained as product of a double stochastic matrix with the cost vector of edges in the optimal tree provided by the Kruskal algorithm.It turns out that the Potters value (P-value) is an element of this class.

Oligopoly games with and without transferable technologies

In this paper standard oligopolies are interpreted in two ways, namely as oligopolies without transferable technologies and as oligopolies with transferable technologies.From a cooperative point of view this leads to two different classes of cooperative games.We show that cooperative oligopoly games without transferable technologies are convex games and that cooperative oligopoly games with transferable are totally balanced, but not necessarily convex.

Bimatrix games have quasi-strict equilibria

In this paper we show that every bimatrix game has at least one quasi-striet equilibrium, i.e. a Nash-equilibrium with the property that every player assigns positive probability to each of his pure best replies.

How to Share Railways Infrastructure Costs

In this paper we propose an infrastructure access tariff in a cost allocation problem arising from the reorganization of the railway sector in Europe. To that aim we introduce the class of infrastructure cost games. A game in this class is a sum of airport games and what we call maintenance cost games, and models the infrastructure costs (building and maintenance) produced when a set of different types of trains belonging to several agents makes use of a certain infrastructure. We study some properties of infrastructure cost games and provide a formula for the Shapley value of a game in this class. The access tariff we propose is based on the Shapley value of infrastructure cost games.

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.

Directed networks, allocation properties and hierarchy formation

We investigate properties for allocation rules on directed communication networks and the formation of such networks under these payoff properties. We study allocation rules satisfying two appealing properties, Component Efficiency (CE) and the Hierarchical Payoff Property (HPP). We show that such allocation rules exist if and only if we restrict ourselves to a class of weakly hierarchical networks. Strengthening the hierarchical payoff property provides a similar result regarding the class of (strongly) hierarchical networks. Such hierarchical networks possess an explicit top-down structure. Subsequently, we discuss several possibilities to model the formation of such hierarchical networks.

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.

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 the corresponding 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.