Gale–Nikaidō–Debreu theorem
E612750
The Gale–Nikaidō–Debreu theorem is a fundamental result in mathematical economics that provides conditions ensuring the existence (and sometimes uniqueness) of equilibrium in certain nonlinear and general equilibrium models.
All labels observed (1)
| Label | Occurrences |
|---|---|
| Gale–Nikaidō–Debreu theorem canonical | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T6710768 — resolving that mention is where its identity was fixed. The disambiguator weighed these candidate entities and picked the highlighted one (or “None”, minting a new entity). This is how homonymy is resolved: the same surface form can point to different entities.
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Gale–Nikaidō–Debreu theorem Context triple: [David Gale, notableWork, Gale–Nikaidō–Debreu theorem]
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A.
Kakutani fixed-point theorem
The Kakutani fixed-point theorem is a fundamental result in mathematical analysis and game theory that guarantees the existence of fixed points for certain set-valued (multivalued) functions, underpinning key existence proofs such as Nash equilibria.
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B.
Knaster–Kuratowski–Mazurkiewicz lemma
The Knaster–Kuratowski–Mazurkiewicz lemma is a fundamental result in combinatorial topology that guarantees the existence of a point common to a family of closed sets covering a simplex under certain intersection conditions, and underlies several fixed-point theorems.
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C.
Glicksberg fixed-point theorem
The Glicksberg fixed-point theorem is a result in functional analysis that extends Kakutani’s fixed-point theorem to certain infinite-dimensional or compact convex subsets of locally convex topological vector spaces.
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D.
Tarski’s fixed point theorem
Tarski’s fixed point theorem is a fundamental result in order theory and lattice theory that guarantees the existence of fixed points for monotone functions on complete lattices, with wide applications in logic, computer science, and economics.
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E.
Kuhn’s theorem
Kuhn’s theorem is a fundamental result in game theory that shows any finite extensive-form game with perfect recall has an equivalent normal-form (strategic-form) representation, ensuring the existence of mixed-strategy equilibria.
- F. None of above. chosen
- G. Unsure - the case is ambiguous/there is not enough information to decide.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Gale–Nikaidō–Debreu theorem Target entity description: The Gale–Nikaidō–Debreu theorem is a fundamental result in mathematical economics that provides conditions ensuring the existence (and sometimes uniqueness) of equilibrium in certain nonlinear and general equilibrium models.
-
A.
Kakutani fixed-point theorem
The Kakutani fixed-point theorem is a fundamental result in mathematical analysis and game theory that guarantees the existence of fixed points for certain set-valued (multivalued) functions, underpinning key existence proofs such as Nash equilibria.
-
B.
Knaster–Kuratowski–Mazurkiewicz lemma
The Knaster–Kuratowski–Mazurkiewicz lemma is a fundamental result in combinatorial topology that guarantees the existence of a point common to a family of closed sets covering a simplex under certain intersection conditions, and underlies several fixed-point theorems.
-
C.
Glicksberg fixed-point theorem
The Glicksberg fixed-point theorem is a result in functional analysis that extends Kakutani’s fixed-point theorem to certain infinite-dimensional or compact convex subsets of locally convex topological vector spaces.
-
D.
Tarski’s fixed point theorem
Tarski’s fixed point theorem is a fundamental result in order theory and lattice theory that guarantees the existence of fixed points for monotone functions on complete lattices, with wide applications in logic, computer science, and economics.
-
E.
Kuhn’s theorem
Kuhn’s theorem is a fundamental result in game theory that shows any finite extensive-form game with perfect recall has an equivalent normal-form (strategic-form) representation, ensuring the existence of mixed-strategy equilibria.
- F. None of above. chosen
Statements (41)
| Predicate | Object |
|---|---|
| instanceOf |
mathematical theorem
ⓘ
theorem in mathematical economics ⓘ |
| appliesTo |
excess demand functions
ⓘ
general equilibrium models ⓘ nonlinear systems ⓘ |
| areaOfApplication |
economic theory
ⓘ
mathematical optimization ⓘ nonlinear complementarity problems ⓘ |
| assumes |
certain sign conditions on principal minors of the Jacobian
ⓘ
continuity of the mapping ⓘ |
| characterizes | conditions for global univalence of excess demand mappings ⓘ |
| concerns |
existence of equilibrium
ⓘ
uniqueness of equilibrium ⓘ |
| ensures |
at most one equilibrium under its hypotheses
ⓘ
injectivity of the mapping under P-matrix conditions ⓘ |
| field |
general equilibrium theory
ⓘ
mathematical economics ⓘ nonlinear analysis ⓘ |
| historicalPeriod | 20th century ⓘ |
| implies |
existence of solution to certain nonlinear equations
ⓘ
global univalence under suitable conditions ⓘ |
| mathematicalDomain |
multivariate calculus
ⓘ
real analysis ⓘ topology ⓘ |
| namedAfter |
David Gale
NERFINISHED
ⓘ
Gérard Debreu NERFINISHED ⓘ Hirofumi Nikaidō NERFINISHED ⓘ |
| provides | sufficient conditions for equilibrium ⓘ |
| relatedTo |
Arrow–Debreu model
NERFINISHED
ⓘ
Brouwer fixed point theorem NERFINISHED ⓘ Kakutani fixed point theorem NERFINISHED ⓘ existence of competitive equilibrium ⓘ global univalence theorem NERFINISHED ⓘ |
| typeOfResult |
existence theorem
ⓘ
uniqueness theorem ⓘ |
| usedIn |
analysis of comparative statics in nonlinear models
ⓘ
proofs of equilibrium existence in general equilibrium theory ⓘ |
| usesConcept |
Jacobian matrix
NERFINISHED
ⓘ
P-matrix ⓘ fixed point arguments ⓘ monotonicity ⓘ |
How these facts were elicited
The pipeline generated the facts above by prompting gpt-5.1 with this entity's name + description and the instruction below.
Instruction
You are a knowledge base construction expert. Given a subject entity and a description of it, return factual statements that you know for the subject as a JSON list of dictionaries(triples), where keys must be "subject", "predicate" and "object". The number of facts may be very high, between 25 to 50 or more, for very popular subjects. For less popular subjects, the number of facts can be very low, like 5 or 10. # Requirements - If you don't know the subject at all, return an empty list. - If the subject is not a named entity, return an empty list. - Include at least one triple where predicate is "instanceOf". - Do not get too wordy. - Separate several objects into multiple triples with one object.
Input
Subject: Gale–Nikaidō–Debreu theorem Description of subject: The Gale–Nikaidō–Debreu theorem is a fundamental result in mathematical economics that provides conditions ensuring the existence (and sometimes uniqueness) of equilibrium in certain nonlinear and general equilibrium models.
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.