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1629708. Theory of Games and Economic Behavior, published in 1944 [1] by Princeton University Press, is a book by mathematician John von Neumann and economist Oskar Morgenstern which is considered the groundbreaking text that created the interdisciplinary research field of game theory. [2][3][4] In the introduction of its 60th anniversary ...
John von Neumann. Game theory emerged as a unique field when John von Neumann published the paper On the Theory of Games of Strategy in 1928. [12] [13] Von Neumann's original proof used Brouwer's fixed-point theorem on continuous mappings into compact convex sets, which became a standard method in game theory and mathematical economics.
Family background. [edit] Von Neumann was born in Budapest, Kingdom of Hungary (then part of the Austro-Hungarian Empire), [ 13 ][ 14 ][ 15 ] on December 28, 1903, to a wealthy, non-observant Jewish family. His birth name was Neumann János Lajos. In Hungarian, the family name comes first, and his given names are equivalent to John Louis in ...
Minimax theorem. Not to be confused with Min-max theorem. In the mathematical area of game theory, a minimax theorem is a theorem providing conditions that guarantee that the max–min inequality is also an equality. The first theorem in this sense is von Neumann 's minimax theorem about zero-sum games published in 1928, [ 1 ] which was ...
System of mathematical set theory. In the foundations of mathematics, von Neumann–Bernays–Gödel set theory(NBG) is an axiomatic set theorythat is a conservative extensionof Zermelo–Fraenkel–choice set theory(ZFC). NBG introduces the notionof class, which is a collection of setsdefined by a formulawhose quantifiersrange only over sets.
Von Neumann–Morgenstern utility theorem. In decision theory, the von Neumann–Morgenstern (VNM) utility theorem demonstrates that rational choice under uncertainty involves making decisions that take the form of maximizing the expected value of some cardinal utility function. This function is known as the von Neumann–Morgenstern utility ...
This variant of backward induction has been used to solve formal games from the beginning of game theory. John von Neumann and Oskar Morgenstern suggested solving zero-sum, two-person formal games through this method in their Theory of Games and Economic Behaviour (1944), the book which established game theory as a field of study. [6] [7]
Cooperative game theory is a branch of game theory that deals with the study of games where players can form coalitions, cooperate with one another, and make binding agreements. The theory offers mathematical methods for analysing scenarios in which two or more players are required to make choices that will affect other players wellbeing. [5]