Tatsuro Ichiishi, Adam Idzik

Equitable allocation of divisible goods and market allocation of indivisible goods.

806

Abstract

The existence of equitable allocations of divisible goods is established. The methods used give divisions of a good into geometrically simple sets, such as simplexes or polyhedral convex cones. Market for indivisible goods is modelled, in which a financial intermediary plays the role as an income re-distributer and each consumer can demand as many goods as he wants subject to his budget constraint, and the existence of a competitive equilibrium is proved. These two seemingly unrelated economic problems are solved by applying David Gale's covering lemma and a dual version of its extension. The extension of Gale's lemma and its dual versions are established here; the proofs are based on Ky Fan's fundamental theorem on coincidence of two set-valued functions.