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

被引：0

作者：

Thanh Le

Cuong Le Van

Ngoc-Sang Pham

Cagri Saglam

机构：

[1] University of Wollongong,Department of Economics

[2] IPAG Business School,undefined

[3] Paris School of Economics TIMAS,undefined

[4] EM Normandie Business School,undefined

[5] Metis Lab,undefined

[6] Bilkent University,undefined

来源：

Journal of Optimization Theory and Applications | 2022年 / 194卷

关键词：

Sperner lemma; Simplex; Subdivision; Fixed point theorem; Gale–Nikaido–Debreu lemma; General equilibrium;

D O I：

暂无

中图分类号：

学科分类号：

摘要：

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.

引用

页码：1072 / 1080

页数：8

共 50 条

[41] A constructive proof of Higman's lemma in Isabelle
Berghofer, S
TYPES FOR PROOFS AND PROGRAMS, 2004, 3085 : 66 - 82
[42] Nontrivial solutions of a nonlinear heat flow problem via Sperner's Lemma
Palamides, P. K.
Infante, G.
Pietramala, P.
APPLIED MATHEMATICS LETTERS, 2009, 22 (09) : 1444 - 1450
[43] Sperner's lemma and zero point theorems on a discrete simplex and a discrete simplotope
Iimura, Takuya
Murota, Kazuo
Tamura, Akihisa
DISCRETE APPLIED MATHEMATICS, 2012, 160 (4-5) : 588 - 592
[44] A proof of Yomdin-Gromov's Algebraic Lemma
Burguet, David
ISRAEL JOURNAL OF MATHEMATICS, 2008, 168 (01) : 291 - 316
[45] A NEW PROOF OF BOREL'S LEMMA IN TWO DIMENSIONS
Li, Dening
ELECTRONIC JOURNAL OF DIFFERENTIAL EQUATIONS, 2015,
[46] A proof of Yomdin-Gromov’s Algebraic Lemma
David Burguet
Israel Journal of Mathematics, 2008, 168 : 291 - 316
[47] Schanuel's lemma, the snake lemma, and product and direct sum in Hv-modules
Vaziri, Yaser
Ghadiri, Mansour
TURKISH JOURNAL OF MATHEMATICS, 2017, 41 (05) : 1121 - 1132
[48] A Proof of Parikh's Theorem via Dickson's Lemma
Koga, Toshihiro
INTERNATIONAL JOURNAL OF FOUNDATIONS OF COMPUTER SCIENCE, 2021, 32 (02) : 163 - 173
[49] GENERALIZING SPERNER'S LEMMA TO A FREE MODULE OVER A SPECIAL PRINCIPAL IDEAL RING
Bullington, Grady D.
JOURNAL OF COMMUTATIVE ALGEBRA, 2012, 4 (03) : 345 - 368
[50] Envy-Free Allocation by Sperner's Lemma Adapted to Rotation Shifts in a Company
Lantaron, Sagrario
Lopez, Marilo
Merchan, Susana
Rodrigo, Javier
Rodriguez, Jose Samuel
MATHEMATICS, 2021, 9 (09)

← 1 2 3 4 5 →