Kuhn’s theorem
E398341
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.
All labels observed (1)
| Label | Occurrences |
|---|---|
| Kuhn’s theorem canonical | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T3910485 — 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: Kuhn’s theorem Context triple: [Harold W. Kuhn, notableConcept, Kuhn’s theorem]
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A.
Szekeres–Lindström theorem
The Szekeres–Lindström theorem is a result in combinatorics that characterizes the maximum size of intersecting families of subsets, serving as a precursor to and special case of the Erdős–Ko–Rado theorem.
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B.
expected utility theory (with John von Neumann)
Expected utility theory (with John von Neumann) is a foundational framework in economics and decision theory that models how rational agents make choices under uncertainty by maximizing the expected value of a utility function.
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C.
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.
-
D.
Tarski’s fixed point theorem
Tarski’s fixed point theorem is a fundamental result in order theory and lattice theory that guarantees the existence of fixed points for monotone functions on complete lattices, with wide applications in logic, computer science, and economics.
-
E.
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.
- 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: Kuhn’s theorem Target entity description: 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.
-
A.
Szekeres–Lindström theorem
The Szekeres–Lindström theorem is a result in combinatorics that characterizes the maximum size of intersecting families of subsets, serving as a precursor to and special case of the Erdős–Ko–Rado theorem.
-
B.
expected utility theory (with John von Neumann)
Expected utility theory (with John von Neumann) is a foundational framework in economics and decision theory that models how rational agents make choices under uncertainty by maximizing the expected value of a utility function.
-
C.
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.
-
D.
Tarski’s fixed point theorem
Tarski’s fixed point theorem is a fundamental result in order theory and lattice theory that guarantees the existence of fixed points for monotone functions on complete lattices, with wide applications in logic, computer science, and economics.
-
E.
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.
- F. None of above. chosen
Statements (45)
| Predicate | Object |
|---|---|
| instanceOf | theorem in game theory ⓘ |
| appliesTo |
finite extensive-form games
ⓘ
games with perfect recall ⓘ |
| asserts | every finite extensive-form game with perfect recall has an equivalent normal-form representation ⓘ |
| assumes |
finite game tree
ⓘ
finite number of players ⓘ perfect recall of information sets and actions ⓘ |
| clarifies |
conditions under which behavior strategies can replace mixed strategies
ⓘ
relationship between extensive-form and normal-form equilibria ⓘ |
| concerns | equivalence of strategic descriptions of games ⓘ |
| distinguishes | mixed strategies and behavior strategies ⓘ |
| domain |
decision theory
ⓘ
mathematical economics ⓘ |
| ensures |
existence of mixed-strategy equilibria in finite extensive-form games with perfect recall
ⓘ
strategic-form representation preserves players’ expected payoffs under behavior strategies ⓘ |
| formalizedIn | expected utility framework ⓘ |
| foundationFor |
refinements of Nash equilibrium in extensive-form games
ⓘ
subgame-perfect equilibrium analysis ⓘ |
| historicalContext | developed in the mid-20th century ⓘ |
| implies |
any finite extensive-form game with perfect recall can be represented as a strategic-form game
ⓘ
behavior strategies are sufficient in games with perfect recall ⓘ |
| influenced | later work on extensive-form equilibrium concepts ⓘ |
| involvesConcept |
behavior strategy
ⓘ
information sets ⓘ mixed strategy ⓘ outcome-equivalence ⓘ perfect recall ⓘ |
| namedAfter | Harold W. Kuhn ⓘ |
| publishedIn | work of Harold W. Kuhn on extensive games ⓘ |
| relatesForm |
extensive-form game
ⓘ
normal-form game ⓘ strategic-form game ⓘ |
| requires |
no forgetting of previously chosen actions
ⓘ
no forgetting of previously known information ⓘ perfect recall assumption ⓘ |
| states | in games with perfect recall mixed strategies and behavior strategies are outcome-equivalent ⓘ |
| supports | equivalence between extensive-form and normal-form analysis under perfect recall ⓘ |
| typeOf |
equivalence theorem
ⓘ
representation theorem ⓘ |
| usedBy |
economic theorists
ⓘ
game theorists ⓘ theoretical computer scientists ⓘ |
| usedIn |
analysis of extensive-form games
ⓘ
existence proofs for Nash equilibrium in extensive-form games ⓘ noncooperative game theory ⓘ |
How these facts were elicited
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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: Kuhn’s theorem Description of subject: 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.
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.