Triple
T131710
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Nash bargaining solution |
E2666
|
entity |
| Predicate | relatedTo |
P37
|
FINISHED |
| Object |
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.
|
E15614
|
NE FINISHED |
How this triple was built (4 steps)
Every LLM step that produced this triple, in pipeline order — named-entity classification, the disambiguation choices (the exact options shown, with the pick highlighted), and the generated description. The batch + timestamp of each is in the Provenance table below.
NER
Named-entity recognition
gpt-5-mini
Instruction
Given a phrase, classify it is english named entity (e.g., persons, organizations, works of art) in Latin script, or not (e.g., literals, dates, URLs, verbose phrases). For disambiguation, the statement where the phrase occurs as object is also given. Please return a JSON object with `phrase` (string, the phrase being analyzed) and `is_ne` (boolean, indicating whether the phrase is a Named Entity).
Input
Phrase: Kalai–Smorodinsky bargaining solution | Statement: [Nash bargaining solution, relatedTo, Kalai–Smorodinsky bargaining solution]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Kalai–Smorodinsky bargaining solution Context triple: [Nash bargaining solution, relatedTo, Kalai–Smorodinsky bargaining solution]
-
A.
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.
-
B.
Theory of Games and Economic Behavior
Theory of Games and Economic Behavior is a foundational 1944 book by John von Neumann and Oskar Morgenstern that established game theory as a rigorous mathematical framework for analyzing strategic decision-making in economics.
-
C.
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.
-
D.
Non-cooperative Games
Non-cooperative Games is John Nash’s seminal 1950 paper that founded modern non-cooperative game theory and introduced the concept now known as Nash equilibrium.
-
E.
Kakutani fixed-point theorem
The Kakutani fixed-point theorem is a fundamental result in mathematical analysis and game theory that guarantees the existence of fixed points for certain set-valued (multivalued) functions, underpinning key existence proofs such as Nash equilibria.
- F. None of above. chosen
- G. Unsure - the case is ambiguous/there is not enough information to decide.
NEDg
Description generation
gpt-5.1
Instruction
Generate a one-sentence description of the target entity. You are given a context triple in the form (subject, predicate, object), where the object is the target entity. # Instructions Use the triple to infer relevant information about the entity. Describe the entity based on what is most defining, well-known. Avoid repeating the information from the triple, unless really essential. # Response Format Return only the sentence: "Description: [one-sentence description of the target entity]"
Input
Entity: Kalai–Smorodinsky bargaining solution Triple: [Nash bargaining solution, relatedTo, Kalai–Smorodinsky bargaining solution]
Generated description
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.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Kalai–Smorodinsky bargaining solution Target entity description: 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.
-
A.
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.
-
B.
Theory of Games and Economic Behavior
Theory of Games and Economic Behavior is a foundational 1944 book by John von Neumann and Oskar Morgenstern that established game theory as a rigorous mathematical framework for analyzing strategic decision-making in economics.
-
C.
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.
-
D.
Non-cooperative Games
Non-cooperative Games is John Nash’s seminal 1950 paper that founded modern non-cooperative game theory and introduced the concept now known as Nash equilibrium.
-
E.
Kakutani fixed-point theorem
The Kakutani fixed-point theorem is a fundamental result in mathematical analysis and game theory that guarantees the existence of fixed points for certain set-valued (multivalued) functions, underpinning key existence proofs such as Nash equilibria.
- F. None of above. chosen
Provenance (5 batches)
The batch behind each pipeline step, in order, with when it ran. Timestamps are batch-level — stages were processed in waves, so the object chain (NER → NED1 → NEDg → NED2) reads in order, but predicate / elicitation batches can sit in a different wave.
| Step | Stage | Batch ID | Status | When |
|---|---|---|---|---|
| creating | Elicitation | batch_69a2520c0f3481908b0ed054a2fca8d0 |
completed | Feb. 28, 2026, 2:25 a.m. |
| NER | Named-entity recognition | batch_69a25785ad5c819097c00f31719fea7e |
completed | Feb. 28, 2026, 2:48 a.m. |
| NED1 | Entity disambiguation (via context triple) | batch_69a2b01814e88190a21f98527b8f9420 |
completed | Feb. 28, 2026, 9:06 a.m. |
| NEDg | Description generation | batch_69a2b0820abc8190b495c6347c989882 |
completed | Feb. 28, 2026, 9:08 a.m. |
| NED2 | Entity disambiguation (via description) | batch_69a2b0db1180819096f569241e07de3b |
completed | Feb. 28, 2026, 9:09 a.m. |
Created at: Feb. 28, 2026, 2:30 a.m.