Scarf’s lemma
E776131
mathematical lemma
result in combinatorial topology
result in game theory
result in mathematical economics
Scarf’s lemma is a fundamental result in combinatorial topology and game theory that guarantees the existence of approximate solutions to certain systems, underpinning proofs of equilibrium existence in economics and related fields.
All labels observed (1)
| Label | Occurrences |
|---|---|
| Scarf’s lemma canonical | 1 |
Statements (40)
| Predicate | Object |
|---|---|
| instanceOf |
mathematical lemma
ⓘ
result in combinatorial topology ⓘ result in game theory ⓘ result in mathematical economics ⓘ |
| appliesTo |
balanced games
ⓘ
cooperative games with transferable utility ⓘ systems of linear inequalities ⓘ |
| consequence |
existence of approximate competitive equilibria in exchange economies
ⓘ
nonemptiness of the core for balanced games ⓘ |
| developedBy | Herbert E. Scarf NERFINISHED ⓘ |
| field |
combinatorial topology
ⓘ
game theory ⓘ general equilibrium theory ⓘ mathematical economics ⓘ |
| guarantees | existence of approximate solutions to certain systems ⓘ |
| hasProperty |
constructive in nature
ⓘ
finite combinatorial formulation ⓘ provides approximate rather than exact solutions ⓘ |
| influenced |
algorithmic game theory
ⓘ
computational general equilibrium analysis ⓘ |
| mathematicalDomain |
combinatorics
ⓘ
economic theory ⓘ optimization theory ⓘ topology ⓘ |
| namedAfter | Herbert E. Scarf NERFINISHED ⓘ |
| relatedTo |
Brouwer fixed-point theorem
NERFINISHED
ⓘ
Kakutani fixed-point theorem NERFINISHED ⓘ Shapley–Scarf housing market model NERFINISHED ⓘ Sperner’s lemma NERFINISHED ⓘ core of a cooperative game ⓘ |
| topic |
approximate fixed points
ⓘ
combinatorial representations of equilibria ⓘ |
| underpins | proofs of equilibrium existence in economics ⓘ |
| usedFor |
constructive proofs of equilibrium existence
ⓘ
proving existence of approximate competitive equilibria ⓘ proving existence of core allocations in cooperative games ⓘ proving existence of equilibria ⓘ |
| usedIn |
proofs of core existence theorems
ⓘ
proofs of equilibrium existence in exchange economies ⓘ proofs of equilibrium existence in production economies ⓘ |
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.