In this paper we introduce a model of an exchange economy with indivisible goods and money. There are many agents each of whom owns one unit of each of nitely many different types of indivisible goods and certain amount of money. Each type of indivisible good is subject to quality...

In this paper we consider a class of economies with a finite number of divisible commodities, linear production technologies, and indivisible goods, and a finite number of agents. This class contains several well-known economies with indivisible goods and money as special cases. It is shown 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 an algorithm is proposed to find an integral solution of (nonlinear) complementarity problems. The algorithm starts with a nonnegative integral point and generates a unique sequence of adjacent integral simplices of varying dimension. Conditions are stated under which the algorithm...

In this paper we prove the following fixed point theorem. Consider a non-empty bounded polyhedron P and a function f from P to P such that for every x in P with f(x) not equal to x there is a ball in P around x such that the inner product of f(y)-y and f(z)-z is nonnegative for any two elements...

In this paper, an algorithm is proposed to find a discrete zero point of a function on the collection of integral points in the n-dimensional Euclidean space R (n). Starting with a given integral point, the algorithm generates a finite sequence of adjacent integral simplices of varying dimension...

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...