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      A direct proof of the Gale–Nikaido–Debreu lemma using Sperner’s lemma

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      Author(s)
      Le, T.
      Le Van, C.
      Pham, N.-S.
      Sağlam, Çağrı
      Date
      2022-09
      Source Title
      Journal of Optimization Theory and Applications
      Print ISSN
      0022-3239
      Publisher
      Springer
      Volume
      194
      Issue
      3
      Pages
      1072 - 1080
      Language
      English
      Type
      Article
      Item Usage Stats
      10
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      5
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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.
      Keywords
      Fixed point theorem
      Gale–Nikaido–Debreu lemma
      General equilibrium
      Simplex
      Sperner lemma
      Subdivision
      Permalink
      http://hdl.handle.net/11693/111580
      Published Version (Please cite this version)
      https://doi.org/https://doi.org/10.1007/s10957-022-02067-2
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      • Department of Economics 724
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