A Direct Proof of the Gale–Nikaido–Debreu Lemma Using Sperner’s Lemma

Journal article: The Gale–Nikaido–Debreu lemma plays an important role in establishing the existence of competitive equilibrium. In this paper, we use Sperner’s lemma and basic elements of topology to prove the Gale–Nikaido–Debreu lemma.

Author(s)

Thanh Le, Cuong Le Van, Ngoc-Sang Pham, Cagri Saglam

Journal
  • Journal of Optimization Theory and Applications
Date of publication
  • 2022
Keywords
  • Sperner lemma
  • Simplex
  • Subdivision
  • Fixed point theorem
  • Gale–Nikaido–Debreu lemma
  • General equilibrium
Pages
  • 1072-1080
URL of the HAL notice
Version
  • 1
Volume
  • 194