Game Theory

Game theory is the study of mathematical models of strategic interactions among rational agents.[1] It has applications in many fields of social science, used extensively in economics as well as in logic, systems science and computer science.[2] Traditional game theory addressed two-person zero-sum games, in which a participant's gains or losses are exactly balanced by the losses and gains of the other participant. In the 21st century, game theory applies to a wider range of behavioral relations, and it is now an umbrella term for **the science of logical decision making in humans, animals, as well as computers.**

Modern game theory began with the idea of mixed-strategy equilibria in two-person zero-sum game and its proof by John von Neumann. Von Neumann's original proof used the Brouwer fixed-point theorem on continuous mappings into compact convex sets, which became a standard method in game theory and mathematical economics. His paper was followed by Theory of Games and Economic Behavior (1944), co-written with Oskar Morgenstern, which considered cooperative games of several players.[3] The second edition provided an **axiomatic theory of expected utility**, which allowed mathematical statisticians and economists to treat decision-making under uncertainty.[4]

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