Theorems
Minimax Theorem
Also Known As Von Neumann Minimax Theorem
Game Theory
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The minimax theorem states that in a two person zero sum game with finitely many pure strategies, there is a value and a pair of mixed strategies, one for each player, such that each player can guarantee at least that value regardless of what the other does. John von Neumann proved it in 1928, founding mathematical game theory.
Facts
StatementFor every two person zero sum game with finitely many strategies, the maximum of the minimum outcomes equals the minimum of the maximum outcomes: max-min equals min-max. 1 Cross-Tradition Connections
Sources
1. von Neumann, Zur Theorie der Gesellschaftsspiele (1928)
John von Neumann, Mathematische Annalen, vol. 100, 1928Mathematische Annalen 100 (1928), pp. 295-320
1. von Neumann, Zur Theorie der Gesellschaftsspiele (1928)
John von Neumann, Mathematische Annalen, vol. 100, 1928Proved By: John von Neumann
1. von Neumann, Zur Theorie der Gesellschaftsspiele (1928)
John von Neumann, Mathematische Annalen, vol. 100, 1928In Branch: Game Theory
Wikipedia: Minimax Theorem
Wikimedia FoundationIn Branch: Optimization, Lead sectionQuote, In Branch: Optimization, Lead section
In the mathematical area of game theory and of convex optimization
Dissenting Readings (1 dissenting reading)
Proved By: John von Neumann
In a 1953 Econometrica article, Maurice Frechet argued that Emile Borel, in papers published between 1921 and 1927, should be credited as the true initiator of game theory ahead of von Neumann, even though Borel himself never proved the minimax theorem. Von Neumann replied in the same issue, defending his own 1928 paper as the first rigorous proof and the founding result of the mathematical theory. The credit for founding game theory is genuinely contested in this narrow sense: Borel raised the questions first, von Neumann proved the theorem first.
A dissenting reading, from Maurice Frechet (1953)Maurice Frechet, Frechet, Emile Borel, Initiator of the Theory of Psychological Games and Its Application (1953), Econometrica, vol. 21, no. 1, 1953
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