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...

In this paper we study competitive outcomes and endogenous coalition formation in a cooperative n-person transferable utility (TU) game from the viewpoint of general equilibrium theory. For any given game, we construct a competitive exchange coalition production economy corresponding to the...

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...

A number of heterogeneous items are to be sold to several bidders. Each bidder demands at most one item. The price of each item is not completely flexible and is restricted to some admissible interval. In such a market economy with price rigidities, a Walrasian equilibrium usually fails to...

We establish a discrete multivariate mean value theorem for the class of positive maximum component sign preserving functions. A constructive and combinatorial proof is given based upon a simplicial algorithm and vector labeling. Moreover, we apply this theorem to a discrete nonlinear...