H. Ben-El-Mechaiekh and R. W. Dimand, A Simpler Proof of the Von Neumann Minimax Theorem, Amer. Math. Monthly 118 (2011) 636-641.Ben-El-Mechaiekh H. and R. W. Dimand, A Simpler Proof of the Von Neumann Minimax Theorem, Amer. Math. Monthly, 118 No. 7 (2011) 636-641....
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...
Theorem:AJourneyThroughDifferent MathematicalContexts TinneHoffKjeldsen CommunicatedbyJ.Gray 1.Introduction ThefirstpurposeofthispaperistotellthehistoryofJohnvonNeumann’sdevel- opmentoftheminimaxtheoremfortwo-personzero-sumgamesfromhisfirstproofof
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 ...
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...
Von Neumann’s application of this topological proof to economics was very influential in post-war mathematical economics and in particular was used by Arrow and Debreu in their seminal 1954 paper on general equilibrium, perhapsthecentral paper in modern traditional economics. ...
(4) The von Neumann algebra A has a faithful representation on a separable Hilbert space. 2 Proof. We first show that (1) is satisfied. Let E be the predual of A, and suppose that E has a countable dense subset {x0, x1, x2, . . .} ⊆ E. Evaluation on the (xi) induces ...
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 ...
VON Neumann algebrasMATHEMATICAL optimizationEUCLIDEAN geometryIn this paper, we establish a new proof to the Von Neumann minimax Theorem in Euclidean spaces. Our key argument relies on standard arguments of convex optimization as well as elementary Euclidean geometric properties.MANSOUR, M. ...
I.Joó, Note on my paper “A simple proof for von Neumann’s minimax theorem” , Acta.Math 44 (1984), 363–365. MATHJoó, I. (1984) Note on my paper “A simple proof for von Neumann's minimax theorem”. Acta Math. Hungar. 44: pp. 363-365...