A Further Generalization of the Gale-Nikaido-Kuhn-Debreu Market Equilibrium Theorem

TL;DR

This paper extends the Gale-Nikaido-Kuhn-Debreu market equilibrium theorem to a broader class of economies with commodity spaces modeled by any Hausdorff topological vector space with a nontrivial continuous dual, generalizing previous results.

Contribution

It generalizes existing market equilibrium existence theorems from locally convex spaces to all Hausdorff topological vector spaces with nontrivial continuous duals.

Findings

Broadened applicability of the GNKD theorem

Extended equilibrium existence results to wider commodity spaces

Provided a unified framework for various topological vector spaces

Abstract

We extend the important generalizations by Yannelis [25] and Cornet et al [7] of the classical result of Gale, Nikaido, Kuhn and Debreu (the "GNKD theorem") regarding existence of market equilibrium, by broadening the applicability of their results, which apply only to economies with commodity space that can be modeled by a locally convex Hausdorff space, to the wider class of economies with commodity spaces describable by any Hausdorff topological vector space with nontrivial continuous dual.