Shapley–Gale theorem
E612745
The Shapley–Gale theorem is a foundational result in cooperative game theory that characterizes stable outcomes in assignment and matching problems, underpinning much of modern market design and matching theory.
All labels observed (1)
| Label | Occurrences |
|---|---|
| Shapley–Gale theorem canonical | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T6710763 — 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: Shapley–Gale theorem Context triple: [David Gale, notableWork, Shapley–Gale theorem]
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A.
Sperner's lemma
Sperner's lemma is a fundamental result in combinatorial topology that guarantees the existence of a fully labeled simplex in certain labeled triangulations, and is widely used to prove fixed-point and equilibrium theorems.
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B.
Kalai–Smorodinsky bargaining solution
The Kalai–Smorodinsky bargaining solution is a cooperative game theory concept that selects a fair agreement between parties by preserving proportional gains relative to their best possible outcomes.
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C.
Erdős–Gallai theorem
The Erdős–Gallai theorem is a fundamental result in graph theory that characterizes which sequences of nonnegative integers can occur as the degree sequences of simple graphs.
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D.
Nash bargaining solution
The Nash bargaining solution is a foundational concept in game theory that defines a fair and efficient outcome for two-party bargaining problems based on axioms of rationality and symmetry.
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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: Shapley–Gale theorem Target entity description: The Shapley–Gale theorem is a foundational result in cooperative game theory that characterizes stable outcomes in assignment and matching problems, underpinning much of modern market design and matching theory.
-
A.
Sperner's lemma
Sperner's lemma is a fundamental result in combinatorial topology that guarantees the existence of a fully labeled simplex in certain labeled triangulations, and is widely used to prove fixed-point and equilibrium theorems.
-
B.
Kalai–Smorodinsky bargaining solution
The Kalai–Smorodinsky bargaining solution is a cooperative game theory concept that selects a fair agreement between parties by preserving proportional gains relative to their best possible outcomes.
-
C.
Erdős–Gallai theorem
The Erdős–Gallai theorem is a fundamental result in graph theory that characterizes which sequences of nonnegative integers can occur as the degree sequences of simple graphs.
-
D.
Nash bargaining solution
The Nash bargaining solution is a foundational concept in game theory that defines a fair and efficient outcome for two-party bargaining problems based on axioms of rationality and symmetry.
-
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 (25)
| Predicate | Object |
|---|---|
| instanceOf |
result in cooperative game theory
ⓘ
theorem ⓘ |
| appliesTo |
assignment games
ⓘ
two-sided matching markets ⓘ |
| assumption | transferable utility in assignment games ⓘ |
| characterizes | stable matchings ⓘ |
| concerns |
assignment problems
ⓘ
matching problems ⓘ stable outcomes ⓘ |
| coreIdea | stable outcomes correspond to core allocations in assignment games ⓘ |
| field |
cooperative game theory
ⓘ
market design ⓘ matching theory ⓘ |
| framework | cooperative games with transferable utility ⓘ |
| guarantees | existence of stable outcomes in certain matching models ⓘ |
| influenced |
design of matching mechanisms
ⓘ
theory of stable matchings ⓘ |
| namedAfter |
David Gale
ⓘ
Lloyd Shapley ⓘ |
| provides | characterization of the core in assignment games ⓘ |
| relatedTo |
Gale–Shapley algorithm
ⓘ
Shapley–Shubik assignment game ⓘ |
| usedFor | analysis of matching markets with monetary transfers ⓘ |
| usedIn |
matching theory
ⓘ
modern market design ⓘ |
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: Shapley–Gale theorem Description of subject: The Shapley–Gale theorem is a foundational result in cooperative game theory that characterizes stable outcomes in assignment and matching problems, underpinning much of modern market design and matching theory.
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.