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Rational choice theory Bounded rationality. Game theory is the study of mathematical models of strategic interaction among rational decision-makers. Originally, it addressed zero-sum gamesin which each participant's gains or losses are exactly balanced by those of the other participants. In the 21st century, game theory applies to a wide range of behavioral relations, and is now an umbrella term for the science of logical decision making in humans, animals, and computers. Modern game theory began with the idea of mixed-strategy equilibria in two-person zero-sum games and its Intdo by John von Neumann. Von Neumann's original proof used the Intro The endgame is a one act fixed-point theorem on continuous mappings into compact convex setswhich became a standard method in game theory and mathematical economics.
His paper was followed by the book Theory of Games and Economic Behaviorco-written Inttro Oskar Morgensternwhich considered cooperative games of several players. The second edition of this book provided an axiomatic theory of expected utility, which allowed mathematical statisticians and economists to treat decision-making under uncertainty. Game theory was developed extensively in the s by many scholars. It was explicitly applied to biology in the s, although similar developments go back at least as far as the s. Game theory has been widely recognized as an important tool in many fields. John Maynard Smith was awarded the Crafoord Prize for his application of game theory to biology. Discussions of two-person games began long before the rise of modern, mathematical game theory. Ina letter attributed to Charles Waldegraveto analyzed a game called "le her". He was an active Jacobite and uncle to James Waldegravea Endhame diplomat.
One theory postulates Intro The endgame is a one act Waldegrave as the true correspondent, but this has yet to be proven.
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This paved the way for more general theorems. Inthe Danish mathematical economist Frederik Zeuthen proved that the mathematical model had a winning strategy by using Brouwer's fixed point theorem. Borel conjectured the non-existence of mixed-strategy equilibria in finite two-person zero-sum gamesa conjecture that was proved false by von Neumann. Game theory did not really exist as a unique field until John von Neumann published the paper On the Theory of Games of Strategy in Von Neumann's work in game theory culminated in this book.]
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