A direct proof of the Gale–Nikaido–Debreu lemma using Sperner’s lemma
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2022-09
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Abstract
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.
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Journal of Optimization Theory and Applications
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Springer
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Fixed point theorem, Gale–Nikaido–Debreu lemma, General equilibrium, Simplex, Sperner lemma, Subdivision
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English