Von Neumann proved the minimax theorem (existence of a saddle-point solution to 2 person, zero sum games) in 1928. While his second article on the minimax theorem, stating the proof, has long been translated from German, his first announcement of his result (communicated in French to the ...
This note provides an elementary and simpler proof of the Nikaid么-Sion version of the von Neumann minimax theorem accessible to undergraduate students. The key ingredient is an alternative for quasiconvex/concave functions based on the separation of closed convex sets in finite dimension, a result...
Von Neumann proved the minimax theorem (existence of a saddle-point solution to 2 person, zero sum games) in 1928. While his second article on the minimax theorem, stating the proof, has long been translated from German, his first announcement of his result (communicated in French to the Ac...
Early in his work, a paper by Borel on the minimax property led him to develop ... ideas which culminated later in one of his most original creations, the theory of games. In game theory von Neumann proved the minimax theorem. He gradually expanded his work in game theory, and with co...
theoremareneglectedaswell.Thispaperwillremedythisandshednewlight ontheseissues. Sincethebeginningoftheninetiestherehasbeenanincreasinginterestinthehisto- ryofgametheory,severalhistoricalpapershaveappearedandmostofthemofcourse mentionvonNeumann’s1928proofoftheminimaxtheorem.Acommonfeaturethough isthatnoneofthesegive...
Our object is to show that von Neumann's proof that hidden variables do not exist is mathematically impeccable, but that he implicitly employed a very restrictive hypothesis, which is that every probability in quantum mechanics must arise from its usual mathematical formalism. However, if a certain...
However, in the 1920s John von Neumann single-handedly invented game theory, introducing the general mathematical concept of "strategy" in a paper on games of chance (Mathematische Annalen 100 [1928] 295-320). This contained the proof of his "minimax" theorem that says "a strategy exists ...
Fréchet, was acknowledged by von Neumann, who had been informed of Borel's work while proofreading his 1937 article. The author primarily stresses the impact of the minimax theorem and sees a philosophical issue raised by the question whether theorems that turn out to be equivalent have the ...
The crucial innovation of von Neumann, which was to be both the keystone of his Theory of Games and the central theme of his later research in the area, was the assertion and proof of the Minimax Theorem. Ideas of pure and randomized strategies had been intro duced earlier, especially...
John von Neumann's Conception of the Minimax Theorem: A Journey Through Different Mathematical Contexts The article is a very carefully elaborated and well argumented historical study of von Neumann's insight into the importance of minimax theorems. In 1928 v... TH Kjeldsen - 《Archive for Histo...