Game theory

Game theory is a branch of applied mathematics that uses models to study interactions with formalised incentive structures ("games"). Unlike decision theory, which also studies formalized incentive structures, game theory encompasses decisions that are made in an environment where various players interact strategically. In other words, game theory studies choice of optimal behavior when costs and benefits of each option are not fixed, but depend upon the future choices of other individuals. It has applications in a variety of fields, including economics, international relations, evolutionary biology, political science, and military strategy. Game theorists study the predicted and actual behaviour 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.


In 1944 Princeton University Press published Theory of Games and Economic Behavior, a book by the mathematician John von Neumann and economist Oskar Morgenstern. It contained a mathematical theory of economic and social organization, based on a theory of games of strategy.
This is now a classic work, upon which modern-day game theory is based. Game theory has since been widely used to analyze real-world phenomena from arms races to optimal policy choices of presidential candidates, from vaccination policy to major league baseball salary negotiations. It is today established, both throughout the social sciences and in a wide range of other sciences.
Game theory has come to play an increasingly important role in logic 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, formalising 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, and has even been used as the basis of a game show called Friend or Foe?.
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.


from Wikipedia