Zur Theorie der Gesellschaftsspiele.

von Neumann, J. (1928). Zur Theorie der Gesellschaftsspiele. Mathematische Annalen, 100(1), 295-320.

Type

Journal article

Intellectual base

Primary research

Year

1928

DOI

10.1007/bf01448847

Link

https://doi.org/10.1007/BF01448847

Cited from

economics_finance, mathematics

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.

• 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.
• 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.

• 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.

Domain-specific

• Minimax Theorem
  • Von Neumann established the foundational finite two-person zero-sum case for mixed strategies in 1928.

Verification

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