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A new proof of the infinite-dimensional Gale-Nikaido-Debreu lemma. (Chinese) Zbl 0957.91063
This paper studies the infinite-dimensional Gale-Nikaido-Debreu lemma introduce by 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 [Ky Fan, in ‘Inequalities III’, Proc. 3rd Symp., Los Angeles 1969, 103-113 (1972; Zbl 0302.49019)] and the minimax theorem [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, A. Mas-Colell and 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.
91B50 General equilibrium theory
54H25 Fixed-point and coincidence theorems (topological aspects)