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Game theory is a branch of mathematics that uses models to study interactions with formalized incentive structures ("games"). It has applications in a variety of fields, including economics, evolutionary biology, political science, and military strategy. Game theorists study the predicted and actual behavior of individuals in games, as well as optimal strategies. Seemingly different types of interactions can exhibit similar incentive structures, thus all exemplifying one particular game.
John von Neumann and Oskar Morgenstern first formalized the subject in 1944 in their book Theory of Games and Economic Behavior.The psychological theory of games, which originates with the psychoanalytic school of transactional analysis, remains a largely unrelated area.
Game theory has unusual characteristics in that while the underlying subject often appears as a branch of applied mathematics, researchers in other fields carry out much of the fundamental work. At some universities, game theory gets taught and researched almost entirely outside the mathematics department.
Game theory has important applications in fields like operations research, economics, collective actionThe economic theory of Collective action is concerned with the provision of public goods (and other collective consumption) through the collaboration of two or more individuals, and the impact of externalities on group behavior. The foundational work in c, political science, psychology, and biologyBiology studies the variety of life clockwise from top-left E. coli tree fern, gazelle, Goliath beetle Biology is the science of life. It is concerned with the characteristics and behaviors of organisms, how species and individuals come into existence, an. It has close links with economics in that it seeks to find rational strategies in situations where the outcome depends not only on one's own strategy and "market conditions", but upon the strategies chosen by other players with possibly different or overlapping goals. Applications in military strategy drove some of the early development of game theory.
Game theory has come to play an increasingly important role in logicIn ordinary language, logic is the reasoning used to reach a conclusion from a set of assumptions. More formally, logic is the study of inference—the process whereby new assertions are produced from already established ones. As such, of particular concern and in computer science. Several logical theories have a basis in game semantics. And computer scientists have used games to model interactive computations. Computability logic attempts to develop a comprehensive formal theory ( logic) of interactive computational tasks and resources, formalizing these entities as games between a computing agent and its environment.
Game theoretic analysis can apply to simple games of entertainment or to more significant aspects of life and society. The prisoner's dilemma, as popularized by mathematician Albert W. Tucker, furnishes an example of the application of game theory to real life; it has many implications for the nature of human co-operation.
Biologists have used game theory to understand and predict certain outcomes of evolution, such as the concept of evolutionarily stable strategy introduced by John Maynard Smith and George R. Price in a 1973 paper in Nature (See also Maynard Smith 1982). See also evolutionary game theory and behavioral ecology.Analysts of games commonly use other branches of mathematics, in particular probability, statistics and linear programming, in conjunction with game theory.
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