Gale’s example in stable matching with couples
E612751
Gale’s example in stable matching with couples is a classic counterexample in matching theory that demonstrates how allowing couples to participate can cause stable matchings to fail to exist.
All labels observed (2)
| Label | Occurrences |
|---|---|
| Gale–Shapley algorithm cannot always find a stable matching with couples | 1 |
| Gale’s example in stable matching with couples canonical | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T6710769 — 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’s example in stable matching with couples Context triple: [David Gale, notableWork, Gale’s example in stable matching with couples]
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A.
Matchmakers
Matchmakers is a popular Ukrainian comedy television series produced by Kvartal 95 Studio that follows the humorous clashes and relationships between two very different families.
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B.
The Perfect Match
The Perfect Match is a romantic comedy film produced by Flavor Unit Entertainment that follows a commitment-phobic bachelor whose views on love are challenged by an unexpected relationship.
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C.
Many Marriages
Many Marriages is a 1923 novel by American author Sherwood Anderson that explores themes of love, sexuality, and personal liberation in small-town Midwestern life.
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D.
The Dancing Couple
The Dancing Couple is a lively 17th-century genre painting by Dutch artist Jan Steen that humorously depicts a boisterous village celebration with dancing peasants and chaotic revelry.
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E.
PairGrid
PairGrid is a Seaborn class for creating multi-plot grids that visualize pairwise relationships across multiple variables in a dataset.
- 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’s example in stable matching with couples Target entity description: Gale’s example in stable matching with couples is a classic counterexample in matching theory that demonstrates how allowing couples to participate can cause stable matchings to fail to exist.
-
A.
Matchmakers
Matchmakers is a popular Ukrainian comedy television series produced by Kvartal 95 Studio that follows the humorous clashes and relationships between two very different families.
-
B.
The Perfect Match
The Perfect Match is a romantic comedy film produced by Flavor Unit Entertainment that follows a commitment-phobic bachelor whose views on love are challenged by an unexpected relationship.
-
C.
Many Marriages
Many Marriages is a 1923 novel by American author Sherwood Anderson that explores themes of love, sexuality, and personal liberation in small-town Midwestern life.
-
D.
The Dancing Couple
The Dancing Couple is a lively 17th-century genre painting by Dutch artist Jan Steen that humorously depicts a boisterous village celebration with dancing peasants and chaotic revelry.
-
E.
PairGrid
PairGrid is a Seaborn class for creating multi-plot grids that visualize pairwise relationships across multiple variables in a dataset.
- F. None of above. chosen
Statements (42)
| Predicate | Object |
|---|---|
| instanceOf |
counterexample in matching theory
ⓘ
example in stable matching theory ⓘ non-existence example ⓘ |
| assumes |
couples have joint preferences over pairs of positions
ⓘ
hospitals or positions have preferences over individual doctors ⓘ participants include single agents and at least one couple ⓘ |
| citedIn |
literature on two-sided matching with complementarities
ⓘ
papers on NP-completeness of stable matchings with couples ⓘ |
| conclusion | no assignment is stable under the usual blocking pair definition ⓘ |
| contrastsWith | classical stable marriage problem without couples ⓘ |
| demonstrates |
instability introduced by joint preferences of couples
ⓘ
limitations of extending Gale–Shapley algorithm to couples ⓘ non-existence of stable matchings when couples are allowed ⓘ |
| field |
algorithmic game theory
ⓘ
economics ⓘ market design ⓘ matching theory ⓘ theoretical computer science ⓘ |
| formalProperty | every feasible matching is blocked by some pair or couple ⓘ |
| historicalRole | early example highlighting difficulties of couples in centralized matching ⓘ |
| implies | Gale–Shapley algorithm cannot always find a stable matching with couples ⓘ |
| involvesConcept |
blocking couple
ⓘ
blocking pair ⓘ complementarities in preferences ⓘ joint preferences ⓘ stability in two-sided markets ⓘ |
| motivates |
complexity results for matching with couples
ⓘ
search for alternative matching mechanisms ⓘ search for weaker stability concepts ⓘ |
| namedAfter | David Gale ⓘ |
| relatedTo |
Gale–Shapley algorithm
ⓘ
hospital–residents problem with couples ⓘ matching with couples ⓘ stable marriage problem ⓘ stable matching problem ⓘ |
| shows |
that a stable matching need not exist in the presence of couples
ⓘ
that standard stability notions can be incompatible with couples’ preferences ⓘ |
| teaches | that complementarities can destroy existence of stable outcomes ⓘ |
| usedIn |
analysis of NRMP (National Resident Matching Program)
ⓘ
design of matching algorithms with couples ⓘ research on hospital–residents matching with couples ⓘ teaching of stable matching theory ⓘ |
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’s example in stable matching with couples Description of subject: Gale’s example in stable matching with couples is a classic counterexample in matching theory that demonstrates how allowing couples to participate can cause stable matchings to fail to exist.
Referenced by (2)
Full triples — surface form annotated when it differs from this entity's canonical label.
Gale’s example in stable matching with couples
→
implies
→
Gale–Shapley algorithm cannot always find a stable matching with couples
ⓘ
linked to: Gale’s example in stable matching with couples