Zur Theorie der Gesellschaftsspiele.¶
von Neumann, J. (1928). Zur Theorie der Gesellschaftsspiele. Mathematische Annalen, 100(1), 295-320.
Cited by¶
5 citations across 5 artifacts.
Each citation links to the sentence it supports in the citing article.
Primes¶
- Minimax Strategy
- In the two-player zero-sum game where it was first formalized, every player has a minimax value, and in finite matrix games with mixed strategies the value is unique and maximin and minimax coincide.
This sourceProves the minimax theorem for finite two-player zero-sum games: with mixed strategies, max-min equals min-max and the game has a unique value.
Supported in partVerified against the publisher's abstract
Only the depositor abstract was readable; it states Max Min = Min Max for the bilinear-form result and that the result answered Borel, but says nothing about uniqueness of value or mixed strategies.
“Dabei ist Max Min = Min Max benützt worden, d. unser relativ tiefer Satz über Bilinearformen.”
- In the two-player zero-sum game where it was first formalized, every player has a minimax value, and in finite matrix games with mixed strategies the value is unique and maximin and minimax coincide.
- Mixed Strategy
- The minimax theorem for two-player zero-sum games provides the dual characterization: the best guaranteed payoff against a smart adversary is achieved by a specific mixing distribution.
Supported in partVerified against the publisher's abstract
Von Neumann 1928 proves Max Min = Min Max for two-person zero-sum bilinear-form games, answering Borel's question: it backs an optimal guaranteed mixing distribution, not the claim's wider 'always available'.
“Borel formuliert die auf Bilinearformen bezügliche Frage für ein symmetrisches 2-Personen-Spiel und stellt fest, daß keine Beispiele für Max Min<Min Max bekannt sind. Unser vorstehendes Resultat beantwortet seine Fragestellung.”
- The minimax theorem for two-player zero-sum games provides the dual characterization: the best guaranteed payoff against a smart adversary is achieved by a specific mixing distribution.
- Saddle Point
- Mathematical optimization and analysis: critical points where the gradient vanishes but the Hessian is indefinite; Lagrangian saddle points characterizing constrained optima (min-max duality). Game theory: von Neumann's minimax theorem and the saddle-point characterization of zero-sum equilibria, where one player maximizes along one axis while the other minimizes along the perpendicular axis.
This sourceProves the minimax theorem, characterizing zero-sum equilibria as saddle points of the payoff function over strategy space.
Supported in partVerified against the publisher's abstract
Proves the minimax theorem (Max Min = Min Max) for bilinear forms, supporting the game-theory clause but not the optimization clause.
“Dabei ist Max Min = Min Max benützt worden, d. unser relativ tiefer Satz über Bilinearformen.”
- Mathematical optimization and analysis: critical points where the gradient vanishes but the Hessian is indefinite; Lagrangian saddle points characterizing constrained optima (min-max duality). Game theory: von Neumann's minimax theorem and the saddle-point characterization of zero-sum equilibria, where one player maximizes along one axis while the other minimizes along the perpendicular axis.
- Zero Sum Game
- Game theory — the canonical case: the minimax theorem applies to finite two-player zero-sum games, the benchmark for pure-conflict strategic analysis.
This sourceProves the minimax theorem for finite two-player zero-sum games, establishing the unique value of the game — the benchmark for pure-conflict strategic analysis.
Supported in partVerified against the publisher's abstract
The paper's own text asserts the Max Min = Min Max result for a two-person (bilinear-form) game, answering Borel — the primary minimax proof, but it does not itself call that result the benchmark for pure-conflict analysis.
“Borel formuliert die auf Bilinearformen bezügliche Frage für ein symmetrisches 2-Personen-Spiel und stellt fest, daß keine Beispiele für Max Min<Min Max bekannt sind. Unser vorstehendes Resultat beantwortet seine Fragestellung.”
- Game theory — the canonical case: the minimax theorem applies to finite two-player zero-sum games, the benchmark for pure-conflict strategic analysis.
Domain-specific¶
Verification¶
Does it exist? Confirmed. This work's DOI resolves to a registered record, which fixes its identity. That is all it fixes.
Does it back the claim? Read against the text for 4 of 5 citations: 4 supported in part. Each verdict is shown under its citation below, with what in the work backs the sentence.
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Registry ID ref:087d95aedb01 · see in the full table