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.
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 NERFINISHED ⓘ |
| 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 NERFINISHED ⓘ |
| relatedTo |
Gale–Shapley algorithm
NERFINISHED
ⓘ
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 ⓘ |
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.