an:01214970
Zbl 0957.91063
Yu, Jian
A new proof of the infinite-dimensional Gale-Nikaido-Debreu lemma
ZH
Math. Appl. 7, No. 2, 243-245 (1994).
00049185
1994
j
91B50 54H25
infinite-dimensional Gale-Nikaido-Debreu lemma; fixed point theorem; minimax inequality; minimax theorem; existence of market equilibria
This paper studies the infinite-dimensional Gale-Nikaido-Debreu lemma introduce by \textit{N. C. Yannelis} [J. Math. Anal. Appl. 108, 595-599 (1985; Zbl 0581.90010)]. Yannelis proves his version of the lemma by Tikhonov's fixed point theorem, while the author provides a new proof using the minimax inequality [\textit{Ky Fan}, in `Inequalities III', Proc. 3rd Symp., Los Angeles 1969, 103-113 (1972; Zbl 0302.49019)] and the minimax theorem [\textit{M. Sion}, Pac. J. Math. 8, 171-176 (1958; Zbl 0081.11502)]. The Gale-Nikaido-Debreu lemma is an important tool in proving the existence of market equilibria [for surveys, \textit{A. Mas-Colell} and \textit{W. R. Zame}, in `Handbook of mathematical enomics', Vol. IV, 1835-1898 (1991; Zbl 0908.90036)]. The author's result suggests that the existence of market equilibria could be established by the minimax inequality and minimax theorem, it is therefore a useful contribution to mathematical economics.
J.Zhao (Columbus/Ohio)
Zbl 0581.90010; Zbl 0302.49019; Zbl 0081.11502; Zbl 0908.90036