In economics, Game Theory is a logical structure of principles and ideas relating to strategic decision making. It applies to industries where competitors need to anticipate/react to each other's actions, because those actions will affect each and every firm.
Clearly this does not apply in market structures that have a high degree of competition, because no single firm in those types of industries is large enough to be significant to any other firm. Instead, Game Theory is most applicable to oligopolistic industries, and to some market structures that are best described as monopolistic competition.
The theory was first developed in 1928 by a mathematician/physicist called John Von Neumann. Interestingly, it's applicability to economic science was not immediately recognized, and it was not until 1944 when Von Neumann coauthored a book called 'Theory of Games and Economic Behavior' that Game Theory became a part of economic doctrine.
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