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 ...
Remarks on acyclic versions of generalized von Neumann and Nash equilibrium theorems theorem for acyclic maps, generalized von Neumann type intersection theorems, the Nash type equilibrium theorems, and the von Neumann minimax theorem. Our... S Park - 《Applied Mathematics Letters》 被引量: 34发表...
minimaxvontheoremconceptionjohn冯诺依曼 Arch.Hist.ExactSci.56(2001)39–68c Springer-Verlag2001 JohnvonNeumann’sConceptionoftheMinimax Theorem:AJourneyThroughDifferent MathematicalContexts TinneHoffKjeldsen CommunicatedbyJ.Gray 1.Introduction ThefirstpurposeofthispaperistotellthehistoryofJohnvonNeumann’sdevel...
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...
Minimax theoremKKM principleKKM spaceFan–Browder fixed point theorema b s t r a c tIn an abstract convex space(E,D;Γ), we show that the partial KKM principle is equivalenttoaFan–Browdertypefixedpointtheoremandthatthistheoremimpliesgeneralizedformsof the von Neumann–Sion minimax theorem.©...
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...
算子环的正式定义出现在冯·诺伊曼1929年的论文“函数运算代数和正规算子理论”(Zur Algebra der Funktionaloperati-oren und Theorie der normalen Operatoren)中.这篇论文还包括了“交换子”(commutant)、“因子”(factor)等重要定义,以及二次交换子定理(double commutant theorem): 是算子环,则交换子也是算子环,...
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...
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...
Established a mathematics framework for quantum mechanics known as the Dirac-von Neumann axioms in 1932 Introduced quantum logics in 1936 Founded the field of game theory as a mathematical discipline and proved his minimax theorem in 1928