Excess demand approach with non-convexity and discontinuity: a generalization of the Gale–Nikaido–Kuhn–Debreu lemma

M. Ali Khan, Richard P. McLean () and Metin Uyanik
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M. Ali Khan: Johns Hopkins University
Richard P. McLean: Rutgers University
Metin Uyanik: University of Queensland

Economic Theory, 2025, vol. 79, issue 4, No 2, 1167-1190

Abstract: Abstract This paper provides a three-fold generalization of the Gale–Nikaido–Kuhn–Debreu lemma, a fundamental result for classical Walrasian general equilibrium theory. It weakens the (i) convexity assumption on the given (excess demand) correspondence, and (ii) the continuity assumption by synthesizing both the majorization and inclusion approaches, and uses these results to derive a (iii) theorem on the existence of a Walrasian equilibrium in an exchange economy with externalities, and non-ordered, non-convex, price-dependent preferences under a weaker continuity assumption that is assumed in the literature. It also highlights a trade-off between the weakened continuity and convexity assumptions.

Keywords: GNKD lemma; Non-convex; Majorization; Inclusion; 91B55; 37E05 (search for similar items in EconPapers)
JEL-codes: C00 C62 D00 D01 D90 O21 (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s00199-025-01641-9

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