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

We introduce a theory on marginal values and their core stability for cooperative games with arbitrary coalition structure. The theory is based on the notion of nested sets and the complex of nested sets associated to an arbitrary set system and the M-extension of a game for this set. For a set...

In this paper we consider cooperative transferable utility games with limited communication structure, called graph games. Agents are able to cooperate with each other only if they can communicate directly or indirectly with each other. For the class of acyclic graph games recently the average...

In this paper we introduce the concept of quasi-building set that may underlie the coalitional structure of a cooperative game with restricted communication between the players. Each feasible coalition, including the set of all players, contains a nonempty subset called the choice set of the...

The Shapley value for directed graph (digraph) games, TU games with limited cooperation introduced by an arbitrary digraph prescribing the dominance relation among the players, is introduced. It is defined as the average of marginal contribution vectors corresponding to all permutations that do...

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 reexamine the well-known assignment market model in a more general and more practical environment where agents may be financially constrained. These constraints will be shown to have an important impact on the set of Walrasian equilibria. We prove that a price adjustment process will either...

This paper introduces a new solution concept for cooperative games with general coalitional structure in which only certain sets of players, including the set of all players, are able to form feasible coalitions. The solution concept takes into account the marginal contribution of players. This...

In the literature various models of games with restricted cooperation can be found. In those models, instead of allowing for all subsets of the set of players to form, it is assumed that the set of feasible coalitions is a proper subset of the power set of the set of players. In this paper we...