We study the existence problem of a zero point of a function defined on a finite set of elements of the integer lattice of the n-dimensional Euclidean space. It is assumed that the set is integrally convex, which implies that the convex hull of the set can be subdivided in simplices such that...

Tucker's well-known combinatorial lemma states that for any given symmetric triangulation of the n-dimensional unit cube and for any integer labeling that assigns to each vertex of the triangulation a label from the set {1,2,...n,-1,-2,....-n} with the property that antipodal vertices on the...

In this paper we present two general results on the existence of a discrete zero point of a function from the n-dimensional integer lattice ℤn to the n-dimensional Euclidean space ℝn. Under two different boundary conditions, we give a constructive proof using a combinatorial argument based...

The triangular array of binomial coefficients, or Pascal's triangle, is formed by starting with an apex of 1. Every row of Pascal's triangle can be seen as a line-graph, to each node of which the corresponding binomial coefficient is assigned. We show that the binomial coefficient of a node is...

In this paper we introduce two values for cooperative games with communication graph structure. For cooperative games the shapley value distributes the worth of the grand coalition amongst the players by taking into account the worths that can be obtained by any coalition of players, but does...

We introduce an efficient solution for games with communication graph structures and show that it is characterized by efficiency, fairness and a new axiom called component balancedness. This latter axiom compares for every component in the communication graph the total payoff to the players of...

We introduce an Owen-type value for games with two-level communication structures, being structures where the players are partitioned into a coalition structure such that there exists restricted communication between as well as within the a priori unions of the coalition structure. Both types of...

We introduce an efficient solution for games with communication graph structures and show that it is characterized by efficiency, fairness and a new axiom called component balancedness. This latter axiom compares for every component in the communication graph the total payoff to the players of...

This paper deals with the optimal provision of infrastructure by means of public-private partnership contracts. Inthe economic literature infrastructure is characterized as a large, indivisible and non-rival capital good thatproduces services for its users. The non-rivalness or nonexcludability...

It is well known that an upper semi-continuous compact- and convex-valued mapping fi from a nonempty compact and convex set X to the Euclidean space of which X is a subset has at least one stationary point, being a point in X at which the image fi(x) has a nonempty intersection with the normal...