Game Theory

Game theory is a domain of applied mathematics that is used in the communal sciences (most notably economics), biology, political science, computer science, and belief. Game theory attempts to mathematically capture behavior in strategic situations, in which an folk success in making choices depends on the choices of others. While initially developed to analyze competitions in which one individual does better at another's expenditure (zero sum games), it has been expanded to treat a wide class of interactions, which are classified according to several criteria.

Traditional applications of game theory attempt to find equilibrium in these games—sets of strategies in which individuals are improbable to change their performance. Many equilibrium concepts have been industrial (most famously the Nash equilibrium) in an attempt to capture this idea. These equilibrium concepts are aggravated differently depending on the field of application, although they often overlap or coincide. This methodology is not without disapproval, and debates continue over the aptness of particular equilibrium concepts, the appropriateness of equilibrium altogether, and the utility of mathematical models more generally.

Although some developments occurred before it, the field of game theory came into being with the 1944 book Theory of Games and fiscal Behavior by John von Neumann and Oskar Morgenstern. This theory was developed extensively in the 1950s by countless scholars. Game theory was later openely applied to ecology in the 1970s, although similar developments go back at least as far as the 1930s. Game theory has been widely recognized as an important instrument in many fields. The first known discussion of game theory occurred in a letter written by James Waldegrave in 1713. In this letter, Waldegrave provides a minimax mixed approach answer to a two-person version of the card game Le Her. It was not until the newspaper of Antoine Augustin Cournot's Researches into the Mathematical ideology of the Theory of Wealth in 1838 that a general game theoretic analysis was pursued. In this work Cournot considers a duopoly and presents a solution that is a restricted version of the Nash equilibrium.