Scarf algorithm
E776130
The Scarf algorithm is a combinatorial method in mathematical economics and game theory used to compute fixed points and prove the existence of equilibria in markets and games.
All labels observed (1)
| Label | Occurrences |
|---|---|
| Scarf algorithm canonical | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T9070908 — 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: Scarf algorithm Context triple: [Herbert Scarf, notableWork, Scarf algorithm]
-
A.
Gale–Shapley algorithm
The Gale–Shapley algorithm is a foundational procedure in mathematics and computer science that computes stable matchings between two equally sized sets, such as students and schools or men and women in the stable marriage problem.
-
B.
Banker's algorithm
Banker's algorithm is a classic deadlock-avoidance algorithm in operating systems that safely allocates resources to processes by simulating and verifying that the system will remain in a safe state.
-
C.
Gale’s top trading cycles algorithm
Gale’s top trading cycles algorithm is a mechanism in matching theory that produces efficient and strategy-proof allocations of indivisible goods, such as in housing markets, by iteratively forming and executing trading cycles among participants.
-
D.
Shapley–Gale theorem
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.
-
E.
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.
- 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: Scarf algorithm Target entity description: The Scarf algorithm is a combinatorial method in mathematical economics and game theory used to compute fixed points and prove the existence of equilibria in markets and games.
-
A.
Gale–Shapley algorithm
The Gale–Shapley algorithm is a foundational procedure in mathematics and computer science that computes stable matchings between two equally sized sets, such as students and schools or men and women in the stable marriage problem.
-
B.
Banker's algorithm
Banker's algorithm is a classic deadlock-avoidance algorithm in operating systems that safely allocates resources to processes by simulating and verifying that the system will remain in a safe state.
-
C.
Gale’s top trading cycles algorithm
Gale’s top trading cycles algorithm is a mechanism in matching theory that produces efficient and strategy-proof allocations of indivisible goods, such as in housing markets, by iteratively forming and executing trading cycles among participants.
-
D.
Shapley–Gale theorem
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.
-
E.
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.
- F. None of above. chosen
Statements (30)
| Predicate | Object |
|---|---|
| instanceOf |
algorithm
ⓘ
combinatorial algorithm ⓘ fixed-point algorithm ⓘ |
| appliesTo |
games
ⓘ
markets ⓘ |
| basedOn | Sperner's lemma ⓘ |
| category |
algorithms in game theory
ⓘ
numerical methods in economics ⓘ |
| developedBy |
Herbert E. Scarf
ⓘ
linked to:
Herbert Scarf
|
| field |
game theory
ⓘ
mathematical economics ⓘ |
| guarantees | existence of approximate fixed point ⓘ |
| hasProperty |
constructive
ⓘ
finite-step procedure ⓘ |
| mainPurpose |
compute fixed points
ⓘ
prove existence of equilibria ⓘ |
| namedAfter |
Herbert E. Scarf
ⓘ
linked to:
Herbert Scarf
|
| relatedAlgorithm | Lemke–Howson algorithm ⓘ |
| relatedConcept |
equilibrium existence theorem
ⓘ
fixed-point theorem ⓘ |
| relatedTo |
Brouwer fixed-point theorem
ⓘ
Nash equilibrium ⓘ general equilibrium theory ⓘ |
| typicalInput | continuous functions on simplices ⓘ |
| typicalOutput | approximate fixed point ⓘ |
| usedFor |
computing approximate equilibria
ⓘ
constructive proofs of equilibrium existence ⓘ |
| uses |
labeling of vertices
ⓘ
simplicial subdivision ⓘ |
| usesMethod | combinatorial techniques ⓘ |
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: Scarf algorithm Description of subject: The Scarf algorithm is a combinatorial method in mathematical economics and game theory used to compute fixed points and prove the existence of equilibria in markets and games.
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.